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You need reads. I am a live player, not a HUD-meister, so I will put it in non-statistical terms. If you have seen EP betting a good percentage of the flops he sees (or at least when he has called a pre-flop raise), and especially if you have seen EP bet flops, show down his hand, and reveal that as of the flop he only had a draw, overcards, or nothing, you might conclude that EP's bet is a continuation bet, and call or raise it on the theory that your AK actually beats a fair part of his range. You also need to consider whether LP is the type of player to fold to your aggression, call, or re-raise and what his likely calling range was pre-flop, as well as what both players are likely to do on the turn if you stay in the hand.
On the other hand, if EP has only bet strong hands on the flop, especially in early position, you may conclude that he's ahead of you and that a fold is in order unless you think that you can force him and LP to fold their hands through sheer aggression, which is also a function of your reads and what they did on prior hands.
(If you have KK or AA, it is somewhat easier, as you will beat a much greater range of hands, but you still want to rely on your reads, i.e., if EP only bets a flop in early position with 2 pair or better, that would be a piece of information you would want to know before jumping in with your overpair!)
I am sure other posters will tell you to get a heads up display and can tell you what statistics to look at to make this determination, and I would endorse that recommendation. But you can also do your reads yourself (as I do). The key is that you process the information from previous hands that you have observed (whether through HUD or your own observation) to determine what that EP flop bet tells you about EP's range.
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