MathNet 2021 — Part 02 Question 85

A fair six-sided cubic die has its faces labeled $1,2,3,4,5,6$. It is rolled three times independently, giving the results $a_1,a_2,a_3$ in order. The probability of the event $|a_1-a_2|+|a_2-a_3|+|a_3-a_1|=6$ is ______.