Weakest gunman's best opening move in a truel

Three people fight a duel-to-the-last: you hit with probability $10\%$, the second shooter with $30\%$ and the third with $60\%$. Shots are taken one at a time in the order you, then the $30\%$ shooter, then the $60\%$ shooter, cycling until one person remains. The others always aim at the most accurate opponent still standing. At whom should you aim your first shot?

Nobody: deliberately miss (fire into the air). If you kill the $60\%$ shooter you face the $30\%$ shooter, who fires first at you; killing the $30\%$ shooter is worse still. By wasting your shot the two stronger players aim at each other, and you get the first shot in whichever duel follows. Working through the states gives a win chance of about $0.204$ for missing on purpose versus $0.202$ for aiming at the best shooter and $0.18$ for aiming at the $30\%$ shooter.