Or to (try and) make it clearer:

I have 3 cards: AKQ. I deal you one, you don't see it.

You have 1/3 chance of having the Ace.

I have 2/3.

I then show you the lowest card I have. No matter what card I show you, you still don't know if you have the ace as I always have either a King or a Queen, the lowest of which I show you. So this gives you no new information and doesn't change the chance of you or me having the ace.