Please explain the math... sorry so lengthy

You are a cyborg in a duel with two other cyborgs. You have a laser beam attached to your arm that fires with 33% accuracy. One of the other cyborgs shoots with 50% accuracy, & the other shoots with 100% accuracy. Each of you is allowed one shot per round & the shooting order starts from the worst shooter to the best shooter. You will shoot 1st, the 50% accurate cyborg will shoot 2nd, & the 100% accurate cyborg will shoot third. If a cyborg is killed, their turn will be skipped. What should you shoot at to maximize your chance of winning?

My answer was to shoot at the ground, eliminating the chance that I hit anyone, thereby eliminating the fact that I'd be shot at next. Then the 50% cyborg will try to shoot the 100% cyborg. If he hits him, I would get to shoot next, with (I thought) a 50% chance of hitting the 50% cyborg since I've spent one of my 1/3 shots making the odds now 1/2.

If the 50% cyborg misses the 100% cyborg, the 100% cyborg will shoot the 50% cyborg. I would then have (again, I thought) a 50% chance of hitting the 100% cyborg.

The book says that instead of me now having a 50% chance of hitting the 100% cyborg, I will only have a 25% chance. I can't figure the math on why 25% instead of 50%.

Thanks for the help! I'm sure this'll be easy for a lot of people but if you could please write the answer in simple terms I'd appreciate it - I struggle quite a bit with the math part. Thank you!