A thousand monkeys at a thousand typewriters... Will eventually write "hamlet". A thousand cats at a thousand typewriters... Will tell you to go write your own damn "Hamlet".
When did the saying get changed? It’s an infinite number of monkeys and typewriters. It’s a reference to the fact that probabilities never go to zero (except in the case of physical impossibilities). Given enough tries (and 1000 isn’t close) random pecking will result in the works of Shakespeare.