Given the infinite monkey typists in the corner of the room, we can safely assume that the probability of them writing the exact text of the book is 1 in 10^10^10. However, since we have already established that the monkeys are in fact predestined to type the exact text, it follows that 1 in 10^10^10 is actually 100%.
QED.
For more on this fascinating topic, visit our sister page on Schrödinger's Cat and how it relates to predestination!
Or, for the mathematical proof of the infinite monkey theorem, click here.