ignore the circle and consider the 3 points around A.
i will use "x" to denote an unknown letter.
The total number of arrangements of xAx = 6 * 1 * 5 = 30
You want to exclude the cases where B is on the left of A
BAx = 1 * 1 * 5 = 5
And the cases where B is on the right of A
xAB = 5 * 1 * 1 = 5
So, there are 10 arrangements where A and B are together.
Probability = 1 - 10/30 = 2/3
Warning my answers on these types of questions tend to be very unreliable