The interval between two adjacent culture classes is at most 1 the probability of art classes is p.

Then the probability that there is no interval between two adjacent culture classes is1-p.

Because there is no interval between culture class and art class, it can be regarded as a whole, and a (3,3) = 6.

Then the overall ranking and the remaining three art categories are A (4,4) = 24, and the total number of events is A (6,6) = 720.

Then 1-P=24*6/720,

So P=4/5.