im not too good of a razz player, but i do ok in horse. i could imagine an excuse for pretty much any move in this situation.
personally i would probably just call, since he didnt raise after he hit the king telling us he probably doesnt have two wheel cards. but i would assume he has worse, he could even have another ace under there and just be bluffing
with 5-A up (i dont know how common bluffs are in razz).
i have to think he has at least one hole card on the wheel which already puts us behind compared to our lowest 3. the danger is his other hole card, if its a blank we're almost sure to out draw him with only 2 cards to go, if not its a crap shoot. and then theres the off chance that he's holding a monster(do those exist in razz?) like 3-4, 2-3, 2-4 and was just a little hesitant when he hit a king(at these stakes i would think he would be better than that).
i dont know how to properly play razz, but if i was villain with something like 3-Q hole cards, i would probably raise when you hit the king even though hero would have a better chance of making the winning hand. then again, i dont know if i would have called $3 when i hit the king.
so, my uneducated conclusion says that the odds
are that we have the best hand but we call instead of raise on the off chance that we are in fact beat. we dont have much to gain from a raise, if he has us beat he'll either re-raise seeing our king, but even if he doesnt have us beat he may call just because of our king.
probably not a very good analysis, but this thread deserves a post, and i'm also curious as to the right move in these situations.