Wizard to ghost?

[meriaugust]

No: HPFGUIDX 86151

Here's a question that popped into my head while reading the posts 
about titles in the WW. People were discussing Nearly Headless Nick 
and why he is refered to as "sir" ie: what had he done to get 
himself a title and then what had happened to lead to his beheading. 
Someone suggested that he perhaps had been discovered to be a wizard 
and was executed for that, but is there any canon evidence to 
confirm that every Hogwarts ghost (or every ghost in the world for 
that matter) was a witch or wizard in life? Moaning Myrtle of course 
was a Hogwarts stuident, and Professor Binns was boring students 
there for years before his death, but what about Nick and the Fat 
Friar and the Bloody Baron and the Grey Lady? All magical (non-
Muggle) people in life? Or is Hogwarts merely a haven for ghosts 
regardless of magical status in life? Did the person have to have 
some Hogwarts connection before they haunt there? What about the 
muggles who become ghosts, if any? Do they fall under the 
jurisdiction of the MoM or are they stuck with figuring out their 
post-biological existence on their own? Any thoughts?