tl;dr Because Great Circles have measure 0, any treatment of probability on them must instead use limits that asymptotically approach Great Circles. Also becaus

tl;dr Because Great Circles have measure 0, any treatment of probability on them must instead use limits that asymptotically approach Great Circles. Also because they have measure 0, such limits don't converge in a consistent fashion. As it turns out, the two most common limit constructions give different results for that particular problem. The closest analogy I can think of is trying to assign a value to the expression 0/0. It doesn't have a value, but you can construct limits that appear to converge to it. One such limit is lim{x/x} as x approaches 0, which tends to 1. Another limit is lim{x log(x)} as x approaches 0, which tends towards 0. Both of these constructions have claim to being the value of 0/0, and they don't reconcile with each other.