What a creative question! Are you asking, Did ghosts forget what it was like to be human, in the transition?
By "believe in", are you asking whether they think humans are capable of extraordinary things- in the manner of believing in God?
Or do you mean, do ghosts believe humans exist?
Tales of ghosts often describe events that indicate they do believe in humans, considering many of them seem to intentionally haunt people and others attempt to communicate with them. Certainly Eva Ibbotson's ghosts believe that people exist, because they interact with them. If the movie Ghost is any indication, some ghosts have unfinished business with humans; this type of ghost probably believes in their existence.
I am assuming you mean "do ghosts believe humans exist", which is fun, but "do ghosts think humans can do great things" intrigues me even more. Stimulating question. Thanks!