If I have 4 ships of the same iniative, and the nearest target is destroyed after the first shot, is the destroyed ship still a legal target and therefore the remaining 3 ships must also shoot at the destroyed ship?

That's the consensus interpretation right now, with one note.

Automated Targeting Priority doesn't necessarily care about *closes* target, just the closest valid range. If there are two Range 1 ships, even the "further away" one is still valid. I know "shortest valid range" will get described as "closest" sometimes, since it's just the easiest way to say it, but just including this for completeness. Not saying folks don't get it or anything like that.

9 hours ago, markrivett said:

is the destroyed ship still a legal target and therefore the remaining 3 ships must also shoot at the destroyed ship?

Another side note clarification: you do have the option to not perform any attack at all when a ship engages. If that destroyed ship has some deterrent like 'ships attacking this one gain a stress' your other three ships can opt to not perform an attack to avoid that downside.

for reference: