An archer shoots an arrow at a circular target of radius $R$. The target is divided into three regions: a central bullseye of radius $\frac{R}{3}$, a middle ring from radius $\frac{R}{3}$ to $\frac{2R}{3}$, and an outer ring from radius $\frac{2R}{3}$ to $R$. Assuming the arrow lands uniformly at random on the target, what is the probability that it lands in the middle ring, given that it does not land in the bullseye?