Probability Trees in Java

I want to write a Hearthstone RNG calculator.

Hopefully, to those that have played the game - this will make a little bit of sense - to those that haven't - sorry! :)

The Problem

The enemy has 4 minions with health [1, 3, 4, 20]

Once the health of an enemy reaches 0 they are considered destroyed and are removed from play (for example - it is impossible for minions to have -1 health)

Once a minion is destroyed/removed from play it cannot be targeted by any more missiles.

I cast the spell Avenging Wrath - which generates 8 separate, random missiles which can hit any of the 4 targets.

Each missile deals exactly 1 damage.

How can I work out the probability that say, the minion with 3 health dies? [x, 0, x, x] How likely is it that it none of them die? [1, 3, 4, 12]

I imagine I will need to use decision trees calculate the outcome after each possible missile hit.

Any chance anyone can point me in the right direction?