Geometry: probability that a random hyperplane separates two random points

I do not have a good intuition for the following problem:

Given three random vectors (unit) $ a, b, n in mathbb {R} ^ d $, elected u.a.r. as points in a unitary sphere, with $ n $ being the normal vector of a hyperplane $ h_n $.

As the dimension $ d $ increased, the probability of $ h_n $ pulling away $ a $ since $ b $ Increase or decrease?