Let us use a quick argument that can scale. I want a monkey to produce a 10,000 character string. Assume I give the monkey a keyboard with only letters/shift key. Thus, he has 52 choices for each space (each letter and its capital version).
So, the probability of him making the string on any given 10k letter run is
P(10k string == my string) = (1/52)^10000 = (1.923*10^-2)^10000. It is tiny. Almost all calculators will round it down to zero. But in reality it is not zero. So what we are saying is that given 1/P(10k string == my string) tries (again, just very large, NOT infinite), this monkey has a really good chance of coming up with my 10k character string.
Since 1/P(10k string == my string) is large but still < infinity, given infinite monkeys and infinite time (or just one monkey and infinite time, but I think we all like the idea of infinite monkeys

), my string will be typed by a random coincidence.
The same scales for the Bibile, Shakespeare, whatever.