Looks like a spot to make continuation bet. If he calls or raises, he probably has you beat so you're done with the hand.
That King might scare him as much as it scares you.
He didn't raise much, and it cost him $.45 to win the $1 in the pot at that point. With no reads, you have his possible range beat more times than not. Maybe not by a huge amount, more often than not.
He's just as likely to have A/Q as A/K. (Of course, K/Q has you beat too.) You still need to bet to see where you stand.