You're right to think that this is a close spot.
A good player will be able to understand that your most likely hands are a mixture of ace-highs, ten-x (Tx) and king-x (Kx) holdings. That good player will then bet good hands and bluffs with a frequency such that you find your river decision, on average, to be a difficult one.
Let's start by considering the situation intuitively, and then if you'd like to extrapolate from that and add some mathematics to the ideas, then I would say bravo to you! It'll definitely be worth your time.
The idea you're struggling with here is the idea of indifference. You claim that you've no reads on this particular opponent, and while that is true, you do know that you're a short stacking player who probably looks to be incredibly weak (in some way... maybe you fold too often, maybe you call too often... I'm not sure) because of your buy-in amount. So, for now, let's ignore that and break down indifference a bit.
Your opponent is putting you on a mixture of hands including a few sets, a few flushes, some ace-highs, some Tx and mostly Kx hands. When he bets all-in, he
should consider that a lot of the time his value bets with Kx hands with which he re-raises pre-flop are less likely to be called as he has a king AND because your most likely calling hand is a king.
In other words, if your opponent's idea is to create a distribution of hands which are indifferent to calling this river bet and your range is as above described, you should be calling with Kx here, absent of any more information. That is because you block your opponent's value betting distribution in a fairly significant way. Yes, he can have A
Q
or A
A
, but he should be considering that when he bluffs. He should have several bluffing combinations as well like A
J
.
As you're both very near the top of the range (you have one of your best possible holdings in this spot) AND you block your opponents distribution that bets for value, I would recommend calling, absent of any other relevant information.
If you can claim that your shot taking or past play has been noticed to the point that your opponent might not bluff here often, if at all, is debatable. What is not debatable is that if you're folding KJ here with these stack sizes with this action that your play is exploitable, i.e. one could simply bet 3 times against you and make you fold far too many of your holdings and if one did this, one would profit against you by bluffing 100% of the time.