Dot Placement

You place three dots along the edges of an octagon at random. What is the probability that all three dots lie on distinct edges of the octagon?

My attempt: An octagon has 8 sides. The probability of choose an edge is random and independent of the other dots so each edge has a \(1/8\) chance of having a dot. It doesn’t matter where the first dot is placed but the second and third have different probabilities which is \(1 \times \frac{7}{8} \times \frac{6}{8} = 42/64\)