Ever heard of "probable cause"?

• Probable cause is where known facts and circumstances, of a reasonably trustworthy nature, are sufficient to justify a man of reasonable caution or prudence in the belief that a crime has been or is being committed. (reasonable man definition; common textbook definition; comes from Draper v. U.S. 1959)
• Probable cause is what would lead a person of reasonable caution to believe that something connected with a crime is on the premises of a person or on persons themselves. (sometimes called the nexus definition; nexus is the connection between PC, the person's participation, and elements of criminal activity; determining nexus is the job of a judicial official, and it's almost always required in cases of search warrants, not arrest warrants)
• Probable cause is the sum total of layers of information and synthesis of what police have heard, know, or observe as trained officers. (comes from Smith v. U.S. 1949 establishing the experienced police officer standard)