"There are a lot of muggle policemen," Pete said soothingly. "Don't fret. It's a fine costume. Tribute. Either. Maybe we just need to help people make the connection. So instead of 'my what a dashing figure William is cutting this evening' they know to think policeman, and then they will undoubtedly come to the correct conclusion."
He wasn't sure he and William were thinking of the same bloke. He, for example, had read stories about a gentleman named Sherlock Holmes, but those had been overwhelmingly fictional. Pete was now going to assume that they were based on Mr. Combes' adventures. Since William seemed so certain. Merlin knew Ravenclaws were rarely certain about things they were not already certain about.