The prosecution has this mans DNA. His relative's DNA likely matched a lot of people. Obviously, they didn't arrest the entire family. It seems likely that they will collect his DNA and attempt to match it to the DNA in his semen. If they get a match, then there is a high likelihood he is the suspect.

More likely, though, they will get a full confession. Serial killers often love to explain their work and take a lot of pride in confessing, because they're really messed up people.