There is no evidence that Arbery intended to steal anything from that house. Under Georgia law, in order to make a citizens arrest, one must have witnessed a felony to have occurred or have immediate knowledge that a felony occurred. Neither father or son observed Arbery commit a felony nor did they have first hand knowledge that he had. They are going to prison for a long time.
As for being suspected of previous break-ins:
“While Gregory McMichael claimed Arbery looked like a suspect in a string of recent burglaries, Glynn County Police Lt. Cheri Bashlor told CNN this week just one automobile burglary in the neighborhood was reported when a 9 mm pistol was stolen January 1 from an unlocked truck outside the McMichaels’ home.”
https://www.cnn.com/2020/05/08/us/ahmaud-arbery-mcmichael-arrests-friday/index.html
Your analysis is wrong. One needs PROBABLE CAUSE that a felony was committed. If my neighbor comes screaming out of her house “that FedEx driver just raped me” and I go get my gun and detain him, I acted upon probable cause. If it turns out later that the woman made it up, it doesn’t matter from a legal perspective . As soon as Arbery sprints out the door, he provided PC for an arrest, as one could presume that his intent was burglary or attempted burglary.