What is the "problem of distributive justice?"
Redistributive justice is a field of study concerned with the "societally fair" distribution of resources in a society. Strictly speaking, this allows for the redistribution of wealth and/or earnings from the wealthy to the poor, and a system of enforced equality of outcome rather than equality of opportunity.
The problem that arises from a policy of redistributive justice is that it unfairly targets segments of the population in order to support other segments. If one poses the argument that the wealthy are required by social morality to support the poor, then the problem begins to occur when distribution reaches an equilibrium; if people know that they can put forth the least amount of effort and gain the same results as those who work the hardest, the burden of support increases for the workers in direct response to the equality of outcome.
Systems of redistributive justice have been implemented in various societies, and in most cases, those societies end up funneling most of the wealth to the leaders (who in a utopian society would occupy the same social status as the workers) instead of focusing on true equality. In the end, the idea that all people are guarenteed the same outcomes, regardless of personal responsibility, is unworkable; the only exceptions come in small societies like communes, where each citizen is personally responsible for supporting the collective and so are motivated to work hard. In larger societies, the concept has proved unworkable.