Terry v Ohio
https://www.law.cornell.edu/supremecourt/text/392/1

New Jersey v. T.L.O. (USSC) 1985)
Public School officials must abide by 4th amendment protection against unreasonable search and seizure but do not have to apply probable cause standard to search student belongings for contraband when have reasonable suspicion to believe they committed an infraction of school rules. If find additional contraband in plain view, do not have to ignore. May seize contraband and pursue a more in depth search of closed compartments if additional evidence in plain view provides reasonable suspicion for that second search for repeated contraband. Scope must be appropriate to the thing to be searched and seized and must not be more intrusive than called for.

http://www.uscourts.gov/educational-resources/educational-activities/facts-...

In criminal cases, "An officer justified in believing that an individual whose suspicious behavior he is investigating at close range is armed may, to neutralize the threat of physical harm, take necessary measures to determine whether that person is carrying a weapon," without securing a warrant and based upon reasonable suspicion, rather than probable cause. Terry v. Ohio, (USSC 1967).

http://www.uscourts.gov/educational-resources/educational-activities/facts-...
Case online. NJ v. TLO (USSC 1985)

"To hold that the Fourth Amendment applies to searches conducted by school authorities is only to begin the inquiry into the standards governing such searches. Although the underlying command of the Fourth Amendment is always that searches and seizures be reasonable, what is reasonable depends on the context within which a search takes place. The determination of the standard of reasonableness governing any specific class of searches requires "balancing the need to search against the invasion which the search entails." Camara v. Municipal Court, supra, at 536-537. On one side of the balance are arrayed the individual's legitimate expectations of privacy and personal security; on the other, the government's need for effective methods to deal with breaches of public order." @337

"We join the majority of courts that have examined this issue [n6] in concluding that the accommodation of the privacy interests of schoolchildren with the substantial need of teachers and administrators for freedom to maintain order in the schools does not require strict adherence to the requirement that searches be based on probable cause to believe that the subject of the search has violated or is violating the law. Rather, the legality of a search of a student should depend simply on the reasonableness, under all the circumstances, of the search. Determining the reasonableness of any search involves a twofold inquiry: first, one must consider "whether the . . . action was justified at its inception," Terry v. Ohio, 392 U.S. at 20; second, one must determine whether the search as actually conducted "was reasonably related in scope to the circumstances which justified the interference in the first place," ibid. Under ordinary circumstances, a search of a student by a teacher or other school official [n7] will be [p342] "justified at its inception" when there are reasonable grounds for suspecting that the search will turn up evidence that the student has violated or is violating either the law or the rules of the school. [n8] Such a search will be permissible in its scope when the measures adopted are reasonably related to the objectives of the search and not excessively intrusive in light of the age and sex of the student and the nature of the infraction. [n9]

This standard will, we trust, neither unduly burden the efforts of school authorities to maintain order in their schools [p343] nor authorize unrestrained intrusions upon the privacy of schoolchildren. By focusing attention on the question of reasonableness, the standard will spare teachers and school administrators the necessity of schooling themselves in the niceties of probable cause and permit them to regulate their conduct according to the dictates of reason and common sense. At the same time, the reasonableness standard should ensure that the interests of students will be invaded no more than is necessary to achieve the legitimate end of preserving order in the schools." @338

4th Amendment, US Constitution
AZ Constitution, Article 2


Illinois v. Gates, 462 U.S. 213 (1983), established the "totality of the circumstances" test - “to make a practical, common-sense decision whether, given all the circumstances set forth in the affidavit before him, including the ‘veracity’ and ‘basis of knowledge’ of persons supplying hearsay information, there is a fair probability that contraband evidence of a crime will be found in a particular place.”
Applies to determining whether a police officer had probable cause to conduct a search and/or seizure, and whether judges had sufficient evidence to justify finding of probable cause to issue warrant.

Also, Mapp v. Ohio; Jenks...

"The ignoble shortcut to conviction left open to the State tends to destroy the entire system of constitutional restraints on which the liberties of the people rest. [n11] Having once recognized that the right to privacy embodied in the Fourth Amendment is enforceable against the States, and that the right to be secure against rude invasions of privacy by state officers is, therefore, dconstitutional in origin, we can no longer permit that right to remain an empty promise. Because it is enforceable in the same manner and to like effect as other basic rights secured by the Due Process Clause, we can no longer permit it to be revocable at the whim of any police officer who, in the name of law enforcement itself, chooses to suspend its enjoyment. Our decision, founded on reason and truth, gives to the individual no more than that which the Constitution guarantees him, to the police officer no less than that to which honest law enforcement is entitled, and, to the courts, that judicial integrity so necessary in the true administration of justice." Mapp. V. Ohio (USSC 1967)

Carroll v. US (USSC 1924) - particularized suspicion of this person who is likely to have committed a felony. Either based upon direct observation of conduct or "reasonably trustworthy information".

Victor v. Nebraska, 511 U.S. 1 (1994), "such doubt as would give rise to a grave uncertainty, raised in your mind by reasons of the unsatisfactory character of the evidence or lack thereof . . . . What is required is not an absolute or mathematical certainty, but a moral certainty.”

There are many good sources online, including Justia. https://www.justia.com/trials-litigation/evidentiary-standards-burdens-proo...