Distance Between Two Random Cutpoints

Lewis is cutting a piece of wood of length $L$ into three pieces. He independently and uniformly at random chooses two cutpoints -- one on the left half of the wood and one on the right half. Let $X_1 \sim \text{Uniform}(0, L/2)$ be the left cutpoint and $X_2 \sim \text{Uniform}(L/2, L)$ be the right cutpoint. What is the probability that the distance between the two cutpoints is less than $L/3$? Compute the answer for $L = 2$ (though note the answer does not depend on $L$).