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If it's checked around, the bet there isn't even repping an ace so much as it's a value bet. If you think no one has an ace, your kings are the best hand and you're betting their value. If you get called you have to think you're up against a baby ace and it's time to let it go. You'll probably get a check on the turn too - I'd check there. Unless you're willing to go in with a huge bluff, that guy who called with his weak ace on the flop isn't mucking on the turn, and he may not even fold to a huge bluff either. Of course he'll probably bet into you on the river if you check the turn, and it's up to you (and the pot odds) whether you think it's worth a call. You also need to read the board: could he be drawing to a flush or straight? If that seems likely then a continuation bet on the turn might be in order, after all.
Incidentally, I wouldn't bet the whole pot on the flop. 1/2 - 2/3 of the pot is enough to get folds from most people if they don't have an ace, and you're more likely to show a net profit from the smaller bet. If you bet half the pot you only need to win 1 time in 3 to break even. (Let's say the pot is $10 and you bet $5... if they fold you win $10, which pays for two more of those bets that are called by someone with an ace. So the less you bet here the better your expectation is for this bet. But you have to bet enough that it's believable that you have an ace, or a high pair just under the ace. If the table is loose maybe closer to 2/3 of the pot is appropriate.)
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