figuring odds when both parties can improve

[AaronBrown]

The good poker calculators figure everything. Here is a quick approximation, similar to ohnonotthat and timex's accounts.

AK beats AJ with Axx on the board 85% of the time, ignoring flushes. So 36% of the time he gets a flush and wins almost all of them. The other 64% of the time, he wins 15% by getting more Jacks than you get Kings. 15%*64% = 9.6%; so that's about 36%+10% = 46% to him. He actually has about 48% due to straights and other possibilities.

I think what's misleading you is thinking you're a huge favorite if he doesn't get the flush, and the odds are almost 2:1 against him getting the flush. Both of those things are true, but they still add up to an almost even hand. Also, he had a good flop, you were about 70% before the flop.