First off, which country are you talking about? This is an international website and subreddit. Second, where are your sources of this information?

First of all, it's important to note the huge increase in total incarceration in the US during the 20th century. This can be attributed to a variety of structural changes including the War on Drugs and other transformations in criminal law like mandatory minimum sentences and three strikes laws. White incarceration has not actually decreased, it has only become a smaller percentage of total incarceration. (http://www.prisonpolicy.org/reports/overtime.html)

Now as to the racial component, you are dealing with a much-debated and relevant topic of inquiry. Michelle Alexander (writer of The New Jim Crow) notably argues in her work that these structural changes emerged in the post Civil Rights era in order to reassert and repackage a racial caste system. You may have seen in the news recently the following quote from Nixon's Chief Domestic Advisor John Ehrlichman which has made headlines recently for shining a spotlight on the racialized motivations of mid-20th century drug policy and its unequal enforcement. “The Nixon campaign in 1968, and the Nixon White House after that, had two enemies: the antiwar left and black people. You understand what I’m saying? We knew we couldn’t make it illegal to be either against the war or black, but by getting the public to associate the hippies with marijuana and blacks with heroin, and then criminalizing both heavily, we could disrupt those communities. We could arrest their leaders, raid their homes, break up their meetings, and vilify them night after night on the evening news. Did we know we were lying about the drugs? Of course we did.” Racial tensions served as fuel for much of the fearmongering that fed the War on Drugs. The history of criminalizing drugs in the US actually has a lot of ties to race and racism (think the Chinese and Opium in the late 19th century).

Nancy A. Heitzeg is also a good source for information in this area. She particularly emphasizes the ways in which economic history have contributed to contemporary racial inequalities in the legal system. For example the impact and legacy of redlining, the disproportionate impact of deindustrialization on Black Americans, and the structural conditions of extreme poverty have all contributed to higher incarceration rates.

This is a huge question and the above is just an introduction, but I hope other people can contribute more.