Even though your question is a very valid one it is only relevant if the questioner believes in God. But in order to ask the question one must be able to show an absolute contradiction to prove that there really was an injustice.
Assuming that there was an injustice does not disprove God's existence. Judaism is a religion that uses this world as a means to enter into the World to Come. This fundamental belief of our existence in this this world gives us a purpose in life - to build on our inherent spirituality and to try and draw closer to God in order to enhance God's presence in this world.
The Sages teach that the Creation of the world is based on Chesed, kindness. God's loving kindness was to bestow the greatest possible good upon His created beings. And the ultimate and greatest good is God Himself.
Therefore, in order for mankind to try and emulate God in this world beings must be created with free-will. To interfere with our free-will contradicts the whole purpose of Creation. That is why it is the norm that the righteous suffer and the evil prosper. To ask God to intervene leaves open the question as to where to draw the line - only Jews? Only murderers?
It is clear that not all who appear "good" are in fact good and vice versa. Tradition teaches that punishment in this world is for any mistakes a person might have made, allowing a person to enter the World to Come. In the same vein long life is not always considered a sign of someone's righteousness. In fact, Jewish Tradition is centered around the fact that physical death is merely a means of gaining entry into the World to Come.
How is one to receive a place in the World to Come? By performing Mitzvot and keeping God's Torah. There are people in this world that deny the very existence of God and they believe that they have no need for the World to Come. However, such people manage to perform plenty of Mitzvot during their lives. This is so even if they did so without any of the correct intentions at all. In this case God has to reward them for their actions with a form of "currency" that fits their lifestyle. One of the ways that God has for rewarding the wicked is to grant them long life and riches in this world. This means that at their Final Judgment, the Heavenly Tribunal can check its records and see that all merits and rewards were paid in the physical world.
The Zohar states, volume 1:146, that no one in the world ever managed to honor his father as much as Eisav did. The Midrash, Bereshit Rabbah 65:12, recounts that Rabbi Shimon ben Gamliel, who was renowned for the way he fulfilled the commandment of Honoring Parents, said "All my life I exerted myself to fulfill the Mitzvah of honoring my father, but I did not attain a hundredth degree of the honor which Eisav accorded his father."
The Sages teach that that is the reason the Eisav was granted such enormous wealth and a longer life than Yaakov.
There is a Midrash that amplifies our inability to fathom the ways of God. "If I have found favor in Your eyes, My God, show me Your ways" In this verse, according to the Midrash, Moses asked God to explain Divine justice to him. The Midrash relates that, in response, God said that He would show Moses two incidents of Divine justice. In the first scene shown to Moses, a soldier dismounts from his horse to have a drink at a small pond. As he gets back on his horse he drops a bag of money without realizing it. The soldier rides off and a teenage boy walking by, sees the money pouch, picks it up and walks away. Later an old man lies down by the pond to sleep. The soldier, who has now realized that he has lost his money, returns to the pond and sees the old man there. He asks the man where his money is and the old man claims not to know. The soldier then draws his sword and kills the man in anger. God said to Moses, "See! Perfect just
