How could Dumbledore convince the Hogsmeade residents that the house which he'd built was haunted?

Question

I think it's significant that the Shrieking Shack was built specifically for Lupin. Dumbledore didn't take a house that already existed in Hogsmeade and insert a tunnel into Hogwarts from it.

"This house -" Lupin looked miserably around the room, "- the tunnel that leads to it - they were built for my use."
_{(Prisoner of Azkaban, Chapter 18, Moony, Wormtail, Padfoot and Prongs).}

It's stated that the Shack became a site of wild legend, somewhere that locals were afraid to go near. It became known as the most haunted building in Britain. Dumbledore encouraged these rumours.

Yet how would the legend of the Shack develop? The residents of Hogsmeade would've known that the Shack was newly built. They would've seen someone from the school doing the construction work. It wasn't a creepy old building when Lupin attended school. It was a newly finished house on a site with no known history of haunting. With or without the strange noises, how did the haunting story ever get off the ground? It seems implausible to me that people could be scared of a house that they presumably knew was just recently put up by the local school.

Answer 1

The rumor almost certainly did not develop right away.

Don't forget, Lupin and his friends were in Hogwarts seven years. That's almost certainly a long enough amount time for a rumor to develop.

Also, although we in the Muggle world are used to having only ancient buildings being haunted, since in HP Universe we know that ghosts are sentient creatures who have the will of their own, perhaps locals thought that the ghosts somehow commissioned someone to make a building for them. The building definitely did not seem to be commissioned by normal humans, since there were no obvious entrances or exits.

A third factor contributing to the rumor's quick spread is that it brought money and tourism to Hogsmeade. Hogsmeade seems to be the wizarding equivalent of a college town and Hogwarts seems to be the primary source of income for most of the towns residents. And presumably Dumbledore spread the rumors through students who came to visit the town. So even assuming that the Hogsmeade residents did not believe the rumors themselves, when they saw the increased income to the uptick in visitors who came to visit the shack due to the hearsay of the students, they had no reason to quell the rumors.