I like Stu's analysis. There are two things I'd like to add to it though:
1. Very broadly speaking, not all hands that beat us take this line. The big bet on the river is not going to be AK often, because people don't tend to bet that big when they're worried about being beat. And people worry about being beat. Similarly, but very different at the same time, most people don't overbet the nuts on the river like this because they're worried about not getting paid off. These two statements aren't mutually exclusive; they just point out that most people don't make really big bets on the river with real hands.
2. There's always going to be the "freak" factor. Some non-zero percentage of the time, our opponent is going to be showing up with a really weird hand that will surprise us. For purely combinatorical reasons, this hand is almost always a bluff (because there are so many more ways to have air than there is to have a big, but weird, hand, e.g. 88 in this hand).
That said, he needs to be bluffing
more than ~35% of the time for you to make this call. I say "bluffing" because there is almost no chance at all that he is valuebetting a worse hand than what you have. While I think AK is a bit unlikely given the action, KT is vastly more so. At midstakes, you can see some good regulars taking this line with KT because they merge their ranges by valuebetting KT here (thus balancing their air and monsters so that people can't bluffcatch with AJ or whatever, but merging is a topic for another day), but here, I seriously doubt it.
So you're looking at a polarized range. From what we know about him, I think his big hands outnumber his bluffs by more than 2:1, so I muck. You should probably consider folding the turn, even, against this guy. Already there, his range probably beats yours and you're pretty often drawing to 5 outs or less. Calling the turn is an OK play if he doesn't valuebet the river lightly, because you need to get a "free" showdown pretty often to make the turn call. Basically, you need him to check behind his A-high hands on the river. If we want to be results-oriented about this hand, then what we learn is that he doesn't - he bluffs his A-high hands on the river. Make a note on that, because that's pretty important.
In fact, I'll take it one step further: The pivotal decision in this hand is on the turn, not the river. The turn call needs to have attached to it a decision on what to do versus a river bet. As in, when you call the turn, you do it because "he will triple barrel bluff me often enough to call down, so I'm calling turn and river, if it comes to that" or "he will bet a lot of his draws on the turn again but shut down on the river, so I'm calling once." If you see what I mean.
From the look of it, your thought process was something similar to the latter above. But then you went ahead and called the river anyway (and "was right" or "got lucky" depending on how you look at it), and I consider that a leak. I should know; I have the same leak. I make a bet with the intention of bet/folding but then when they shove I somehow manage to talk myself into calling anyway, and I know
I shouldn't. It's just... It's just... "Oh, just one more call and then I'll find out."
So yeah, plan the river play on the turn.