As far as I could tell, the chances depend on your sim's mood -- the game will tell you your chance of success. That being said, what usually happens for me is that I don't pay attention, try to pick a lock right in front of the Constable, get thrown in the stocks myself, then once I get out, try to pick the lock again, and am successful. So maybe try to do it when no one is around to see you do it, and try to get your sim's focus level as high as possible.