I thought about this one some more, going more of a math route.
Like ChuckT said, you're either way ahead or way behind (wa/wb).
47 unknown cards, two of them being Kings. 2/47, or about 1/24 that any one card will be a King.
There are three other players so there's about a 6/24 chance. That's about a 1/4 chance of someone holding a King, and actually it's going to be worse than that because all the action would indicate better than average hole cards.
With $5.10 up for grabs and better than a 50/50 shot at being the best hand I'd be comfortable make a nice bet at the pot.
Also, the odds
of someone having the third king are equal to the odds of someone having a Q, and if they have a Q they probably have a worse kicker.
The more I think about it, the more confident I am that betting is the proper move.