Fiery Justice — ruling 1

You choose how many targets Fiery Justice has and how the damage is divided as you cast it. Each target for its damage-dealing effect must receive at least 1 damage.

Fiery Justice — ruling 2

If some (but not all) of the targets become illegal, the original division of damage still applies, but no damage is dealt to illegal targets. If all targets become illegal, including the target opponent for the life-gaining effect, Fiery Justice doesn't resolve. If each target for the damage-dealing effect becomes illegal while the target for the life-gaining effect remains legal, that player gains 5 life even though no damage is dealt.

Fiery Justice — ruling 3

The target opponent for the life-gaining effect may also be a target for the damage-dealing effect. If this happens and the damage brings that player's life total to 0 or less, the life-gaining effect will raise their life total above 0 again before the player would lose the game.

Fiery Justice : règles, fonctionnement et interactions (MTG)

Fiery Justice is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Fiery Justice deals 5 damage divided as you choose among any number of targets. Target opponent gains 5 life.

How it works : Fiery Justice

Original English text — Wizards of the Coast / Scryfall

#1March 14, 2017· Wizards of the Coast
You choose how many targets Fiery Justice has and how the damage is divided as you cast it. Each target for its damage-dealing effect must receive at least 1 damage.
No other card is named in this ruling.
#2March 14, 2017· Wizards of the Coast
If some (but not all) of the targets become illegal, the original division of damage still applies, but no damage is dealt to illegal targets. If all targets become illegal, including the target opponent for the life-gaining effect, Fiery Justice doesn't resolve. If each target for the damage-dealing effect becomes illegal while the target for the life-gaining effect remains legal, that player gains 5 life even though no damage is dealt.
No other card is named in this ruling.
#3March 14, 2017· Wizards of the Coast
The target opponent for the life-gaining effect may also be a target for the damage-dealing effect. If this happens and the damage brings that player's life total to 0 or less, the life-gaining effect will raise their life total above 0 again before the player would lose the game.
No other card is named in this ruling.