If I understand your proposition correctly, your 100 box case goes like this:
1. Start with 100 boxes, one of which contains the $100 note. 2. Select one box, but do not open it. 3. Remove 98 boxes, known to be empty, from the remainder of the set.
At this point, we have two boxes, one of which contains the note. With no other evidence, the probability is exactly 0.5 that the initial selected box is the one you want. The removal of empty boxes raises the probability from an initial one-in-a-hundred, up to one-half, after step 3. The only way it can get higher is to remove the last empty box, when the probability becomes exactly one!
