The assumption that conviction rates by a demographic match actual criminal acts by that demographic is the Occam's Razor outcome, and thus since it by definition can't be proven is either way automatically is the one assumed to be most likely true without evidence indicating otherwise. There is good evidence to indicate black males accused of crimes are convicted more often then others accused of crimes but I've never seen anything credible to indicate the rate is so high as to close that gap, and Occam's Razor rules in absence of that, in this case that black males commit more violent crimes then other racial/gender demographic groups. Discard that and you must essentially discard all other criminal demographics, including that men re more likely to commit rape then women, because the same logic applies.
Most rapes are committed by men is unprovable, or at least not practically provable currently. But it is a logical inference of most convicted rapists being males and of most claims of rape accusing males of perpetuating them. It is not practically provable, but many things aren't and yet must still be discussed. I can't prove that anyone will die of old age in the next year, but I can strongly support that conclusion.
Whites are statistically arrested more often than blacks in Florida (since we have been discussing Florida all this time) for a large majority of crimes committed. This is the raw total number of arrests and not as a function of their respective population distribution. However, we are supposed to assume that the high conviction rates are due to blacks committing these crimes in such higher numbers than whites that, by nature, blacks must be some sort of criminal race. Florida's statistics on numbers of arrests made (which I've linked below) bears this out -- that whites are typically arrested roughly the same or more often than blacks for a large number of crimes.
So then we need to ask, why are blacks more likely to not only be convicted, but to be thought of as more likely to commit crimes? Certainly, as a percentage of population, blacks are statistically more likely to commit certain crimes than whites (notably robbery more than others). However, given that more whites are arrested by raw total, and that blacks are typically given harsher sentences for the same crimes, and that blacks are typically convicted at higher rates in general, I don't think you can simply throw up your hands, claim Occam's Razor precludes drawing any conclusions and call it a day.
Edited to add: because of my lookup of the specific number of arrests, I take back my claim that blacks are arrested more often. The data does not seem to bear this out except for a few select crimes.