Zeus believes Percy stole the Master Bolt because Percy is the demigod son of Poseidon, Zeus's brother, and he is afraid Percy would use it against him.
Percy is Zeus's rival, which makes him think that he might have stolen the master bolt.His adversary is Poseidon. They frequently disagreed about who should reign over Olympians. Percy Jackson was not claimed by Olympus, hence stealing the Master Bolt is impossible.
At first, Poseidon wants to seize power from him and uses his own son to do so, which is possible because Percy, as a son of Poseidon, can (like other demigods) reach locations where gods cannot due to things like courtesy and magical boundaries. Gods are geniuses (in the traditional sense of the word), and their presence often defines the nature of the land they reign over, hence demigods are used in their fights and missions.
Furthermore, in Rick Riordan's Percy Jackson and the Olympians trilogy, Percy is wrongly accused by Zeus of taking the Master Bolt.