The Jumbled Skate Rack

Closing up in the dark, a rink attendant finds six ice skates on the floor: two of size $8$, two of size $9$, and two of size $10$. Unable to read the labels, he ties them into three pairs uniformly at random. A pair is usable if its two skates differ by at most one size. What is the probability that all three pairs turn out usable?