Pretend the book Pinocchio only has 999 total letters in sequence.
The first option on this page http://www.dave-reed.com/Nifty/randSeq.html
is set to "999".
The second option is set to "1".
The third option contains all 26 English alphabet letters.
If the "Click to Generate" button was continually pushed for eternity, would the results (sequences of 999 letters);
1. Eventually write the book Pinocchio.
2. Never write the book Pinocchio.
3. Write infinite copies of the book Pinocchio.
? ? ?
I think the answer is that it would write infinite copies of the book Pinocchio.
Eternity is a long time. Start with the first letter of the book. Since the probability of the correct first letter showing up at the beginning of a 999 letter sequence is not identically equal to zero, it will eventually show up. So let's say it does show up, then you have to look at the 2nd letter to see if it is correct. If it isn't, then you have to keep pushing the Generate button until the correct 1st letter shows up and then check again. Since the probability of both showing up is non-zero, eventually you'll have the correct first 2 letters. You can see how this process would continue to at least until the first correct 999 character sequence is generated.
The process then has to produce 2 correct 999 charter sequences. Even after achieving the first 999 character sequence, the first letter of the 2nd will probably not be correct. Oh well, you've got eternity. Keep banging away. until you get both a correct 1st sequence and the correct next 1st letter, then on to the 2nd. Etc.
It seems important for this conclusion that a) the probability of any letter showing up in any particular position is finite and b) the the number of letters in the Pinocchio book is finite.