If I may, Rawls did confuse "arbitrary" and "random."

'Arbitrary' refers to an act of a human being that is ungoverned, that fails to take into account anything other than the wants of the actor. It is the precondition of injustice in interactions among human beings--as Locke correctly apprehended.

'Random' refers to outcomes that are unaffected by actions of human beings. The allotment of "natural assets" is random, not arbitrary. That puts their distribution outside considerations of (in)justice (though advancements in science are starting to make that distinction less rigid).

That might seem to suggest that 'distributive justice' should thus become the extent to which the distribution of attainments reflects the distribution of such assets. That would be Nozick's position. Yet, for Rawls society is justified in intervening in that process to achieve justice, as 'fairness'.

Even if the distribution of those assets is random, not arbitrary, one could still agree with Rawls that the closest there is to a moral claim to attainments based on them is the "legitimate expectations" of the society of which one is member. So he argues that a Liberal society should determine the legitimate expectations of the distribution of attainments, regardless of the distribution of natural assets, based on 'fairness', which is based in turn on (his interpretation of) the tradition of Liberal thought, resulting in his two principles of justice.

Nozick mostly just reiterated Locke. The radical individualism he endorses follows from a 'State of Nature' that has humans living as isolated beings. Nothing could be more ludicrous. If there is one thing that is certain about 'human nature', it is that we are social beings: we have always lived together in groups we have come to call societies, and presumably we always will. That precludes basing

justice on life as it might be lived by humans who are not social beings.