The Blind Archer

A very sharp, consistently skillful blind archer aims for the center of a circular board and shoots 2 arrows. He is usually close to the center but never hits it for sure; each shot lands independently, with the same distribution every time. The archer is told that his first shot is better than his second. He then shoots one more arrow. What is the probability that this 3rd shot is the best shot among the 3?
(i.e., the probability that the 3rd arrow lands closer to the center than both of his first two shots)