> Yes, but without evidence you aren’t going to jail, and if you do you can sue for wrongful arrest.
You can sue anyone, anytime, for anything, but even if charges aren't filed or a court dismisses them at the preliminary hearing stage for lack of sufficient evidence, wrongful arrest suits against police are very difficult.
> "Probable cause" relates to searching or entering private property.
It also relates to arrest. The Fourth Amendment provision applying the standard explicitly applies to searches and seizures of persons, houses, and effects. Arrest is seizure of one’s person.