I'm having difficulty finding my source right now, but it appears that in cases of homicide by someone unknown to the victim, a police officer is the perpetrator in between 1 in 3 and 1 in 4 incidents. These statistics don't consider whether the killing is justified; they just observe that if people know of someone who was killed by a stranger, there's a 1-in-3 or 1-in-4 chance that stranger has a uniform.
And as we know, people's perceptions of safety are more important than actual statistics. We rewrote the nature of air travel in response to 9/11.