I believe the world is fair, but it is not just. Fairness means the laws of science and the laws of human behavior are consistently applied to everyone. If you are poor, life will be this way. If you are rich, life is that way. If you are black, white, gay, straight, religious, atheist, or anything, you will go through life with various handicaps and benefits. It’s fairly applied to everyone. The best you can do is work with this system and push it more toward justice.
The world is not just. It is blindingly obvious how unjust it is. I don’t need to even justify that. While I believe most of us have an innate understanding of what justice is, I do not think there is actually an external source for the concept of justice. Perhaps it is socially or evolutionarily built into us. Perhaps a little of both. The world is unjust and the best we humans can do is push it more toward justice.