Strategic Question, what to do with A-K facing a reraise???

I lost a hand with A-K today and I'm just wondering how you all would of played it.

In the big blind I'm dealt A-K, two players limp one from early and one from middle position, another middle postion player raises to 5 times the BB, I reraised him 3 times his bet, which he thought about for a long time and finally went all in, essentially reraising me 3 1/2 times my raise.

This happened at a lower stakes table, not even $1/2, I thought for awhile and I began to think possibly he has AA or KK, but I thought he just as likely could have QQ, I think if it had been several hundred dollars I had to call I would of folded, but maybe not. Anyways I called and even though I paired my King and Ace on the flop and turn, I lost to pocket Aces.

My question is how many people would of folded A-Ko in that situation? I had only been at the table about 30 minutes, I had seen the player play marginal hands like K,J and A-8, but maybe he hadn't seen anything better than that. I had no reason to believe he had pocket Aces, but I hate to always assume players have junk, because it's how you get burned.

I haven't been playing too long, very rarely have I been in a situation where I had to call all my money with A-K and didn't feel good about it. Also does anybody know what the chances of having A-K and facing pocket Kings or Aces are??? they can't be very good can they?

Thanks for the feedback