Cards dealt to other players when calculating odds

Imagine this situation:

You deal two cards to yourself and two cards facedown to an empty seat. You can't see the cards in the empty seat.

What are the odds that the next card to be dealt off the deck is an ace if you hold:

1) an ace? 3 out of 50
2) two aces? 2 out of 50
3) no aces? 4 out of 50

Do the two cards in the empty seat matter? No -- you don't know what they are, so the probability remains the same from your point of view. Sure, the empty seat could have one or two aces -- but you can't possibly know that when you're figuring out your probability.

The same holds true when you're calculating probabilities at the table -- you don't know what the other players have in their hand, or what they folded. But their hands don't matter because to your point of view, there are 50 remaining unknown cards (or 47 on the flop, etc.).

I guess a simpler way to think of it is: you aren't calculating the odds based on how many cards are in the deck. You are calculating the odds based on how many cards are left that are unknown to you.

I preferred Magic's more mathematical explanation, but I get the point. It's hard to 'see' why they aren't counted but if that's they way probability works then that is fine by me.