Ok, Mr. Infinity Master Person, answer me this: if an infinite number of monkeys sit at an infinite number of typewriters in an infinite three dimensional universe and each produce an infinite string of text, what is the probability that one of them produces infinitely many copies of the complete works of Shakespeare, one after another?
Probability = 0, presuming all of the typewriters have English letters.
Reasoning:
If there's an infinite amount of monkeys, infinite things happen (presumably simultaneously). Seeing as there's infinite of everything, the one in there throws it all off. There would be an infinite amount of monkeys typing infinitely many copies of the complete works of Shakespeare. Thus there wouldn't be ONE monkey producing Shakespeare, there'd be infinitely many monkeys typing up infinitely many beautifully-timed sonnets.

Then again, life tends to fiddle with things a bit, and it's practically guaranteed that somehow the monkeys would figure out something better to do (like start a revolt, and throw their infinite typewriters at each other until they realized that throwing their poo is a lot more fun).
~D-Draw