Why did the investigator know that X is involved, yet know nothing about them?

And whatever they did was enough to quickly get the attention of the investigators.

It's to avoid the risk of having healthy people's Psycho-Passes get clouded by criminal investigations.

As I worked as a psychiatric examiner and assisted in investigations and such, my main focus shifted to criminal research before I knew it.

When a detective gets deeply involved in an investigation, sooner or later, the Sibyl System starts keeping an eye on them just like it does with the criminals.

Huh? While investigating an unsolved case, Public Safety Bureau Special Case 102, his Crime Coefficient rapidly increased.