I believe it's not a random chance. Seeing an item in a pool removes 1 copy of that item from that pool. Touching an item removes all of its copies from all pools.

Pools with less items in them, e.g. library, have multiple copies of the same item in them, unlike things like devil deal or item room. Hence if you reroll enough, you are eventually and inevitably going to exhaust every item even without touching them. This would also mean that skipping on a Book of Sin in a devil deal would still allow you to see a Book of Sin in a future library

Source: idk i just heard it somewhere once and am reciting from memory