Law Enforcement officials often work with percentages, and it is usually a known perpetrator rather than an unknown person. But, this is not always the case. I remember a case of a missing boy in Montana, Zach Ramsey, the police were convinced that the boy was "missing" due to a situation with a Mother and BF. They didn't really investigate too much.
The killer was actually this random guy, living in the area. Nathanial Barr. He had a history of child molestation. He was caught several years later, in the same town, after trying to molest another boy.
So, if the perpetrator in this situation is just a completely random person, it is almost impossible to figure out who it is...it sounds like there really isn't a lot of information, or the police are not releasing much, if they have a POI.
Even in the Adam Walsh case, they really had no clue who had taken Adam, even after finding his body. They believe his killer was a drifter, Toole.
How do you investigate from an absolute zero sum? If this is what they have at this point...