bet the flop.

if he calls you and checks the turn, this is where you check behind.

looking at his line though you are obv beat.

i also might fold preflop depending on the villian, this is kind of a reverse implied odds spot.

ok if you hit your ace over his jj qq w/e you will never really ever win a big pot. however if you hit your ace or like A K X and he has a set, you pretty much always lose a big pot.

the king can get you in trouble too, is QQ stacking off on a king high flop?