How to avoid hostility during brawl in Markarth?

Thanks for all the help, but it was something totally different. I answer my own question because without knowing about my current equipment this is impossible to answer.

I forgot that I was wearing the ebony mail from a previous quest that had an enchantment that inflicts poison damage to nearby opponents. This triggered the hostility from the guards. Removing the ebony mail solved the problem and I could end the fist fight victorious.