Macbeth believes in the witches’ predictions and is foiled by putting faith in their seeming impossibility; Othello believes the “ocular proof” Iago manages to provide; Claudio and Don Pedro believe Don John’s subterfuge because they believe they can trust their own eyes; those shipwrecked on Prospero’s island all have different views of what the external world appears to hold; Lear fails to discern real love from its semblance in fine

sounding words.

And Hamlet, unlike all of these folks, seeks for more than one sort of proof before he takes any rash action. He acts mad, to see what Claudius will do; he is suspicious of everyone, and finds spies everywhere; he creates this elaborate ruse to watch Claudius' reaction to a similar dramatized situation.

But it's not like it all comes out right because Hamlet was more sceptical, or tried to be more thorough. We do know that Claudius is guilty, and in the cases I mentioned above, the "proof" or "truth" that the protagonist believed in was actually false.