I see many people had this WA. Can someone give me a hint about it?
I think it will be useful for others.

Since one paragraph says that "Each time a duelist may aim at any other alive duelist or purposely shoot in the air."

But the next one says that "The first one (let's call him A) always hits his target and always aims at the best of the living rivals."

Does it mean A always hits the guy who has greater shot accuracy?

This is a problem with possible loops in decision. That means your decision will be based on others' decision, which might  again be based on yourself. I think the best way to solve this sort of problems is to use ITERATION.

I believe that some people could solve this directly. If you are like this, please post your idea or formula, I want to know it very much.

During iteration, we must pay attention to the initialization value. If you have a bad init-value, you will not be able to  move even one step in this problem. In my opinion, the init-value could be set as: when someone is starting a duel, then he could win this duel with prob 1.

By the way, iteration will stop very quickly, as the calculation is unusual: there is function "MAX". So do not worry about the complexity of the problem.

At last, some test-data here:

1.0 0.8 0.5
0.30000000 0.17777778 0.52222222

1.0 0.5 0.0
0.75000000 0.25000000 0.00000000

1.0 1.0 0.0
0.50000000 0.50000000 0.00000000

1 0.9 0.8
0.11000000 0.08265306 0.80734694

1 0.99999 0.99998
0.00001000 0.00001000 0.99998000
(Suprising or not?)

1 0.0001 0.0002
0.99975002 0.00014998 0.00010000

So, Good luck.

Pay attention: players can shot in the air!

1.0 1.0 0.0

What means
"The draw to determine the order of the shots is
considered to be fair, that is, the order of the shots is
unknown in advance"
Does it means that player must choose to whom shoot before
knowing order of the shots?

Please, explain, why a man with smallest precision must not shoot before killing one of others, and give me some examples for testing my program