How would you illustrate justice under Islam?

I would cite two examples from the era of the companions.

Umar ibn al-Khattab

Ibn Wahb reported a woman in San’a (Yemen) cheated on her husband with another man; the woman’s son was present when she was cheating; she said “This boy will expose us!"

So the boy was killed jointly by the man who was cheating, another man, the woman and her servant. They severed the body parts and hid them in baggage to throw in a well.

One was caught and admitted to the killing along with the rest of them.

A letter was written to Umar Ibn Khattab (ra) as to what to do.

He wrote back saying:

والله لو أن أهل صنعاء اشتركوا في قتله لقتلتهم أجمعين

By Allah if the People of San’a (capital of Yemen) shared in the his killing, I would implement the capital punishment on all of them

This justice brings tranquility to the victims under the Islamic System unlike Western systems that regularly acquit accomplices.

Shurayh

When Ali Ibn Abi Talib set out for the battle of Siffeen, he lost a shield. When the battle was over and he returned to Kufah, he found the shield in the possession of a Jewish man who was selling it in the marketplace.

He said to him: “O Jew, this shield is mine, I did not sell it or give it away.”

The Jew said: “It is my shield and it is in my possession.”

Ali said: “Let's go to the judge.”

So they went to Shurayh, and Ali sat beside Shurayh while the Jew sat in front of him.

Shurayh said: “Speak O Ameer Al-Mu’mineen.”

He said: “Yes. I say that this shield that is in the Jew’s hands is my shield. I did not sell it or give it away.”

Shurayh said: “O Ameer Al-Mu’mineen, give me proof.”

He said: “Qunbur (the freed slave of Ali), Al-Hasan and Al-Husayn will bear witness that this shield is mine.”

Shurayh said: “The testimony of the son for the father does not count.”

Ali said: “The testimony of a man who is one of the people of paradise does not count? I heard the Messenger of Allah (saw) say, ‘Al-Hasan and Al-Husayn will be the leaders of the youth among the people of Paradise.’”

The Jew said: “The Ameer Al-Mu’mineen brought me to this judge and this judge is ruling against him? I bear witness this is the truth; I bear witness there is none worthy of worship except Allah and Muhammed is the Messenger of Allah and the shield is your shield. You were riding on your dusky camel, heading towards Siffeen; you dropped it at night and I picked it up.”

Ali said: “Since you admit it, it is yours” and he gave him a horse too.

Shurayh later said he saw him when he went out to fight the Khawarij with Ali at Nahrawaan.

[Alee Ibn Abee Taalib, Dr. Alee Muhammad As-Sallaabee, Vol. 1, p. 395]