First things first - to see a flop with K8, you must've got in cheaply because you aren't going to be playing it if there's a raise in there. So you can probably rule out anyone having QQ, AA, AK, KK and even AQs.
You have K8 and the flop comes:
Chances are you are leading here, if there hasn't been a raise pre-flop which there won't have been. The only hand you have to fear at this point is A8 and the chance of someone holding the case 8 with an Ace is remote.
Turn is a 3.
Ok, still assume you have the best hand here. However, anyone who limped in with pocket 3's will probably let you know about it right here if you didn't already push them out on the flop. Anyone else with a rag Ace is still going to be in the pot.
Now, assuming the river is another Ace which you said. This is where (if you didn't force everyone out on 4th Street) you should slow down, anyone who has been calling you all the way will probably have a ragged Ace, you should check-call here to be safe. You've already gotten enough into the pot already and you can be thankful that you got lucky with a poor hand on the flop - if you are beat by a bigger full house here - unlucky, just look back at your betting structure and determine what you could have done to force him out of the pot.
Action: Check-Call. Don't fold a full house on 5th street UNLESS the bet made easily indicates that he does indeed have the bigger boat.
Ie let's say that there is $12,000 in the pot.
Its you to act and you check.
The other guy raises all in for $38,000.
You have $18,000 left. This is where you FOLD.
Lets say its the same pot, same size but you have $64,000 in chips.
The same guy moves all in to the $12,000 pot for $20,000. At this point i would consider calling, not only for the small chance that you might take the pot (if hes bluffing) but to see just what he was holding in his hand.
9 times out of 10 though, you will take this down before the river if your betting is correct and you aren't up against someone who is slowplaying the nuts (if that happens, tough shit).