Prosecution of a murderer

So I have a brief question on the act of murder and how this will be dealt with within an anarcho-capitalist society.

How would a judge go about murder? Since the individual who has been murdered cannot go to court. The only ground on which I can think that a judge would prosecute a murderer then is because of the common well-being, “society”. But since “society” is not really a category within an anarcho-capitalist framework, on what grounds would a murderer be prosecuted?