The courts
probable cause
The standard for an arrest, a search warrant, or an indictment: enough facts for a reasonable person to believe a crime occurred or evidence will be found.
In full
Probable cause is more than suspicion and much less than proof. The Fourth Amendment requires it, supported by oath, before a warrant may issue. A magistrate reviews the officer's affidavit and decides independently, at least in theory; the practical strength of that review is a long-running subject of criticism and reform.
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A plain-language explanation for civic education, not legal advice. When in doubt, the official source named above controls.