So. What if the serial killer kills his/her wife/husband and then hires our private eye main character to solve the case. THEN the serial killer kills all the suspects as the main character discovers them and presents them to the client/serial killer (I guess as client updates or something? This part is your job).
SO THE SERIAL KILLER IS THE LAST PERSON CONNECTED TO THE KILLING LEFT ALIVE AND THE PRIVATE EYE MAIN CHARACTER FIGURES IT OUT BUT ALSO HAS TO FIND A WAY TO NOT LET THE SERIAL KILLER KNOW HE/SHE KNOWS!!!
ok, that's free. Go with it!