[DiogenesLamp]

The killers witnessed no crime.

The citizens witnessed the crime of trespass, and had reason to believe the recurring trespasser whom they had seen on several videos spanning several months, was the thief.

Yes, they had probable cause.

[AnotherUnixGeek]

The citizens witnessed the crime of trespass

The killers did not claim to have seen their victim commit any trespass. Stop making things up.

And after you stop making things up, go read the definition of trespass under Georgia law, and understand why the killers could not have known that their victim was in any way guilty of criminal trespass on someone else's property.