Archery Rotation

Three archers, Lena, Mia and Nora, hold a sudden-death shootout for a single gold medal. Lena shoots first, then Mia, then Nora, and the rotation repeats in that order until somebody hits the bullseye. Every shot, by any archer, hits the bullseye with probability $1/3$, independently of all other shots. The first archer to hit the bullseye wins.

What is the probability that Lena wins the medal? Give the exact value as a fraction.