I'm confused too. I'm not at my game now so if you are kill him and let us know what happens.
I'm pretty confused too and I'm right at my PC, so hold on a second while I try it...
EDIT: Ok, I made myself a nice dagger, snuck into the back of Belethor's shop during the day and murdered him while he was still on duty. 72 in-game hours later, nobody has taken over the shop and nobody in the game has taken notice.