It's still 20%. I was thinking about this a while ago in the context of poker. If you draw a card from a deck, look at it, and it is an ace of spades, and then you draw another card from the deck, and don't look at it, what is the chance that that it is ace of hearts? Is it 1/51, because now there are only 51 cards in the deck? No, it is still 1/52, because you could've drawn any other card the first time, so you don't fundamentally affect the probabilities. Here's the interesting thing, if you search through the deck, and intentionally withdraw the ace of spades the first time, and then randomly draw a card, now there is a 1/51 chance it is an ace of hearts. You can confirm this with simulations, and in fact this comment gets any traction I'll write a short python script to confirm it, and link a github repo here. So did your intentionality change probabilities? No, actually the answer is pretty simple, but it's deceptive in a similar way to the monty hall problem.