A Clone of me, in a parallel universe

Here is an interesting argument to prove that, somewhere far, far away, there is a planet which has life. It has humans and animals just like they are on earth. Not just that, It further goes to argue that, in some other planet, somewhere far away, there is an exact replica of myself, writting this, right now!!

Assumptions: The space is infinite, which has been proved to some extent by experimental data of cosmic rays detection.

Argument: The basic argument is, in an infinite space, anything is possible!!

In particular, what is the probability that life exists on another planet. It is some number which is not zero but infinitely small and very close to zero. But, since space is infinite, the probability of life in another planet approaches one. Another ways to see it, in a sample space where infinite number of events can happen, the probability of any arbitrary event happening, out of infinite events is "1". So If I pick that event to be, life exist somewhere else. In an infinite space, it surely is true.

Still not convinced, ok try this: Imagine in a bag, there are infinite number of balls with different weights. What is the probability that at least one ball in that bag weighs 1 pound?