Originally Posted by double_u
I think it would be logical for most people to press for more info, even out of curiosity. I think TTG was probably trying to juggle how much dialogue they could put it, and decided to go with lines that aren't repetitive and show more of the character being talked to. Like CarScar said about Katjaa being more worried about Kenny. Or like Kenny more focused on making sure that his family was safe and didn't care once he knew Lee wasn't touching kids.
I think it would be logical in the normal world since murder is such an extreme occurrence, but three months into the apocalypse people don't care anymore. No one talks about their previous jobs beyond the first few episodes, most don't mention their family or anything at all that happened before the apocalypse because it just doesn't matter anymore. As Lee says in episode 3: :"Not much use in describing people by who they were". Everyone accepts that murder may become commonplace now, and they've been with Lee for three months, they know he's a good man and and know they can trust him.
It's still somewhat of a touchy subject, but it's not important enough to need further details anymore other than "I killed a guy."