Kolmogorov didn't cap it predraw with a 1 card draw. His hand isn't as good as you're afraid it is, almost certainly it includes an 8. "f" doesn't have you beat, he checked and called before the last draw. You can figure that your 87542 is good about 50% of the time against K. (Look at all the one card draws that include an 8. Most of them fit this pattern - four cards to improve, two ways to a better 8 then yours, one way to a 9, and one way to a worse 8.) I don't like breaking this hand up when I think you win ~40% of the time ("f" draws out one of you 20% of the time) by standing pat. I also don't like checking and calling with a pat hand at this point. It gives K a ridiculously easy value bet with any better hand and you never win more money when you're ahead.

You should raise this street.

You have two opponents who will call your bet when you're winning. You only get three bet by hands that you know for sure you can break against. Putting in two extra bets on this street does suck when you are losing, but I think thats very rare case - there are very few hands K started with that now make a 7.

Basicaly, I think the pot is big enough that breaking your hand isn't worth the risk of losing the pot when your hand was good. Once you decide that, I like betting your marginal hands out of position, which includes checkraising this street and betting the river.