Three random dots on different sides of a square

Each of three dots is put on one of the four sides of a square, with the side chosen uniformly at random and independently for each dot. What is the probability that no two dots share a side?

$\tfrac38$. The first dot can go anywhere, the second must avoid its side (probability $\tfrac34$), and the third must avoid both used sides (probability $\tfrac24$), giving $\tfrac34\cdot\tfrac12=\tfrac38$.