CMIMC 2019 Combinatorics and Computer Science Problem 5

In the game of Ric-Rac-Roe, two players take turns coloring squares of a 3 \times 3 grid in their color; a player wins if they complete a row or column of their color on their turn. If Alice and Bob play this game, picking an uncolored square uniformly at random on their turn, what is the probability that they tie?