I have a fair cubical die with faces numbered 1, 2, 3, 4, 5, 6, and I throw it three times. What is the probability that the difference between the largest score and the smallest scores I get is two or less? What is the probability that this difference is exactly two?

What are the answers to the same problems if I use a fair octahedral die, with faces numbered 1, 2, 3, 4, 5, 6, 7, 8?