If I remember correctly, CJ's friend called him about the murder of the black prostitute. How would the movie have worked had another "unimportant" murder taken place that night and his friend chose that one instead? This detail is why I didn't guess the end.
shareMy guess is he had setup everything so that his friend would pick this murder. From the start, he was planting seeds in his friends' head "look for a murder with no killer that I can set myself up in". So after the thought was sufficiently planted, he killed the girl and it turned up for his friend to choose.
In a way it is very lucky that one murder was not overshadowed by another on the same night or a different night. Perhaps also, if his friend had taken him to a different murder he would have thought of some reason not to do that one and wait for the one he had committed to pop up.