Its weird but in a lot of novels that include palace intrigue there would usually be one prince that conspiracies with a foreign power and almost every God dam time they kill off all the workers in the area even if its in their living quarters hell they kill their mistress too. This is retarded as hell when all of it could be avoided by talking in a safer location. I mean the palace has a lot of workers but 10 people going missing especially in a area as strict as the heart of a nation is bound to be found out in days. Now as Emperor if you have a gut feeling that something is about to happen and all of a sudden 20 servants is killed by your 3rd son and he is generally calm wouldn't some wtf go into your mind.
People in power usually kill off lower people then themselves like they are ants and it’s thought to be normal in fictional worlds so people don’t care about it in novels in real life it would be different cause the royal censors would get the prince in trouble for doing that for no good reason
Maybe the “third prince” or whoever has built up a reputation as being cruel, ruthless, and merciless, so nobody bats an eye when a bunch of his workers go missing. They’d probably chalk it up to the dead workers messing up and incurring the prince’s anger.
I know about those with horrible reputation but that doesn't change that there should be at least a decent amount of suspicion if the murders intensify around the time you are unease. Mind you that the emperor typically went through all the intrigue himself so he should have somewhat decent intuition