# 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?