 Brownian hitting probability of a ball

For $d\ge 3$ and $|x|>\epsilon$, stop the harmonic function $u(x)=|x{|}^{2-d}$ at the two boundaries of $\{\epsilon <|x|<R\}$. Bounded optional stopping gives the probability of hitting the inner sphere first as $(u(x)-u(R))/(u(\epsilon )-u(R))$. Letting $R\to \infty$ gives the displayed formula; a finite hitting path is contained in some finite-radius ball.