White people are just more hard working than other races as a result the benefits they receive are proportionate to the amount of effort they put in thus society rewards them.
I would argue that this whole idea of white privalige is based off an African American viewpoint which is influenced by the past actions of Jim Crow laws and slavery etc . If you were to look at the word white privalige ? What does white even mean ?
Does it mean fair skin which East Asians , Arabs have etc so thus are they also beneficiaries of white privalige even though they themselves have been subject to intense racism and hysteria ?
Does it mean any person who's ancestors is from Europe? If so does mean that Eastern Europeans who constantly face discrimination are also beneficiaries of white privalige?
The whole idea of white privalige is flawed and based of the opinions of people who want to put the blame for their actions on others.
To use your example bluntly.
The white man would obviously be treated better than the black man as his people don't commit the majority of crime even though they are a minority of the population.