What is Justice?
The question itself, IMHO, is a bit off the mark, sort of like asking what Life is ... or worse, what is the purpose of Life. A better question might be how to arrive at a decision that is Just - does that beg the question? Welll... somewhat, but that response itself does as well, after a fashion, too often it is made while seeking to pretend to complete ignorance of opinion and pretends to purity of intent while re-asking 'What is Justice?', as if that question can erase what you already know it to be, in order to fake a blank slate to begin from.
Like most pretentions of non-prejudice... sorta silly.
The subject of justice is actually one which is going to be more defined by what you already know and understand, than by any answers received from asking what justice is. A person who has a certain philosophy already in place in their mind, will already have an image of what they will recognize as being just - or unjust - stubbornly in mind, and any pretense to the contrary, is probably just that. A pretense.
Thracymachus didn't have to open his yap to Socrates, for his ideas on what Justice was, to be known. And as Socrates's long build up to answering his own question showed, his philosophy had already determined what he considered Justice to be, long before he admitted as much. Ditto for Machiavelli, Rousseau, Kant, and that judicial purveyor of pretentious vapidness (who set me off this time, and has set me off before), Stephen Breyer.
Justice itself is a dynamic process, much more of a result, or a report upon results received from particular processes, rather than a root and guiding principle for shaping a determination of Justice; your guiding philosophy is what defines and determines what justice will seem and be.
Justice depends upon, and displays, what your prior and more fundamental ideas of the nature of Man and the Universe are, and any attempt to change what you suddenly realize 'Justice' should be defined as, and how to 'practice it', are, and unavoidably will be, shallow pretenses, not to be taken too seriously, unlikely to play out in practice, and even less likely to last much longer than the standard new years fitness resolution will last.
If you want to really understand what Justice is, let alone practice it, you need be sure that your first concern involves seeking out, practicing and examining what Reality is and how to respond to it; what Truth is and how you determine it, and what (if any) Oughts are implied by the various IS's which life brings your way.
If you are looking for an answer to 'what is justice', with the expectation that the answer is going to clear things up and enable you to go around pronouncing various situations just or unjust - you're probably fooling yourself, and possibly doing so consciously. But if you do want to understand what can reasonably be called a just, or unjust, decision or situation, you need to understand the process which produces what reasonable people can say with a straight face, was a just decision, and a simple 'answer', isn't going to found, nor would it do the trick if it was found.
That being said, I've been reading or re-reading materials ranging from Hammurabi to the big three (Socrates, Plato & Aristotle), to Cicero, Augustine, Aquinas, and Machiavelli, Hobbes, Locke, Montesquieu, Blackstone, Burke, Adam Smith and the Founders, and even into the black pits of Rousseau, Kant & Hegel, on up to the recent misfires of Murray Rothbard and the libertarians - hey, gotta do something while unemployed - so prepare to dive in to the nature and requirements of Law, Gov't, Rights and the Justice they do, or don't, bring to light.