Not necessarily. There is a big disparity in race of murder victims. The most common murder is black on black. There are more black murder victims than white ones, though blacks make up a smaller proportion of the population. On that basis you would expect more blacks than whites to be incarcerated for murder. The full statistical analysis is complicated. In particular, having the money to hire a good lawyer may be a key explanatory variable.
These observations do not necessarily generalize. It is certainly possible different dynamics are in play for different types of crimes.