I think you are making assumptions that are different from my assumptions from what I saw in the video and from news reports I heard. News reports said that Arbery had three gunshot wounds, one to the hand and two to the chest, not that he was shot three times. The shotgun seemed to go off once during the struggle without hitting anyone. When the struggle began for the shotgun, the person taking the video turned away to get a picture of the hammer that Arbery dropped just before getting to the truck. As the camera view came back up you can see the smoke from the shotgun blast when the background was just the sky. When the video was back on the struggle, the barrel was pointed between the two men and they were still fighting for the shotgun. I assume that the shotgun was a semi auto, but will have to look at the video again. The elder McMichael (a retired police officer and investigator for the DA after retirement from PD) also had a gun that was concealed carry until he pulled it out to go help his son. It was a 357 magnum revolver. What I assume happened: The elder McMichael shoots Arbery and hits him in the chest. The shotgun goes off (several possible reasons that this could happen) hitting Arbery in one of the hands he is holding onto the barrel with and then hitting him in the chest. The video shows Arbery falling, but no more shots being fired. The elder McMichael saw Arbery enter the house under construction (burglarized so often cameras were installed inside) and called 911 before Arbery took off running. That is all the probable cause you would need in Georgia to make a citizens arrest and hold him for the police. If I was trying to stop someone I believed was a criminal, I would be armed too, if it was possible.
“...(burglarized so often cameras were installed inside)….”
Except that the homeowner has stated that nothing was ever stolen from the house under construction. The only thing happening was Lookie Lous wandering through.