Given 1 homicide in 100k for 100sq miles called "rural" vs 1 homicide in 100k for 5 sq miles called "urban", your odds of being in proximity of a homicide are much higher in the urban area. 20 times more likely.
Given 1 homicide in 100k for 100sq miles called "rural" vs 1 homicide in 100k for 5 sq miles called "urban", your odds of being in proximity of a homicide are much higher in the urban area. 20 times more likely.
This doesn't stand up. Crime statistics are measured after the crimes happen; whatever effect might be due to proximity has already taken place.
Consider: in your example you say two places have equal per-capita homicide rates but one is 20x denser. It follows that the denser area will have 20x more people "in proximity" to any given homicide, and therefore that P(victim|proximity) must be 20x lower compared to the rural place.
The way you've done the math only makes sense if everyone "in proximity" of a homicide was equally likely to be a victim, but given equal per-capita rates that can't be the case.