Life is not improbable.

[Heywood]

When you throw in infinities you can have things with a positive probability that still never come to fruition even after infinite number of trials.

If you have an infinite number of trials, by definition you'll exhaust every possibility.

Negative Esquilax.

Some infinities can be insufficient.

Imagine a circle. Now imagine an infinite number of rays originating at the center of the circle and passing thru every point that makes up the perimeter. At the perimeter those rays, as they pass thru each point which makes up the circle are "touching each other". However once they go beyond the perimeter those rays continue to diverge. The farther away from the perimeter the more diverged from each other those rays become. So far so good?

Now draw a larger circle around the first one. There are an infinite number of rays coming from the smaller circle but that infinite number of rays is insufficient to go thru every point that makes up the perimeter of the larger circle. In that space between the divergent rays will exist points that make up the larger circle that have no rays going thru them.

You would think that because you have an infinite number of rays...you would have enough to go thru all the points that make up the larger circle....but you do not.