Your opponent holds ace-king as well, in clubs and spades. You both have the ace-high straight, so you're level.
A third heart lands. With your ace of hearts you now have four hearts, and your opponent holds none, so only you can improve.
Nine hearts are left among the 44 unseen cards, so 20.5 times in 100 you win the whole pot, and the other 79.5 times you split it. You can't lose.