Kings vs Showing Ace(s) in 7 stud

[Fraubump]

Just based on random distribution, if you hold a pair of kings to start in 7 stud (and no ace kicker), in which situation are you most likely to be up against a starting pair of aces?

One Ace Showing
Two Aces Showing
Three Aces Showing

Now let's take it a step further: assume everyone goes to a showdown: by the end of the hand, in which of the above scenarios is it most likely that someone will have a pair of aces by the showdown?

It is tempting at times to raise Kings into multiple board aces, but I'm wondering whether my intuitive sense of the probabilities is wrong. Obviously having a pair of kings against 4 board aces is a sweet situation.