Harford's Investigation
Harford figures out the possibility of an intruder in the prince's office.
He immediately reported it to the prince. The prince, however, told him to not make a fuss about it and end up alerting everyone.
'Try to catch the culprit quietly' is what he was told. And so, the entire job was dumped solely onto his head.
With a green light from the prince, the butler went off to the administrative building to find any leads.
First and foremost, the time of intrusion. There's a long time span between the time he locks the office and the time he returns the next morning. He doesn't know the precise time it happens. Anybody could sneak in from the late evening until early morning the next day.
His prime suspects are obviously the guards patrolling the building. They're the closest to the building and the easiest ones to commit the crime.