Brinegar v. United States
Probable cause exists where "the facts and circumstances within their [the officers'] knowledge and of which they had reasonably trustworthy information [are] sufficient in themselves to warrant a man of reasonable caution in the belief that" an offense has been or is being committed.
An officer's subjective intent or belief is irrelevant in determining probable cause. Only what a reasonable officer would believe matters.
A mistake of fact or law is okay as long as it is reasonable for an officer to make.
Probable cause requires more than just reasonable suspicion, but it does not require evidence that would justify a conviction.
Anonymous tips alone cannot establish probable cause, but they can when combined with the totality of the circumstances. Especially important in such determinations are whether the informant is credible—likely to be telling the truth—and reliable—likely to have knowledge. Thus, the veracity of the informant and his basis of knowledge should be analyzed.
Note that just because an anonymous tip turned out to be true does not mean that it was credible. The totality of the circumstances must establish probable cause before conducting the search, not after. This can be done by corroborating parts of a tip that do not require infringing upon one's reasonable expectation of privacy.