I guess the answer depends on his 3b IP %. If we think it's bluff heavy, lots of weak Axs, SC, baby PP that he 3bet, then we can probe turn with reasonable success.

But on this board, virtually all of his 3b value range can at least call 1 bet, it's almost impossible for him to not have at least a piece. And you'd think his air like A5dd or 22 would've thrown out a flop cbet. So he's got some kinda something, even if it's AJo. If you're willing to fire t and r (if r was a blank), then you can get some more folds like Tx,but I'm not too excited about it. JJ is prob still calling at least some of the time.

As played, the A slams his range better than ours. River is easy c/f.

I feel probe would not be correct and would more so be a bluff if we bet vs JJ and QQ

Fine to probe bet so long as we are super cautious with our sizing. We would literally bet around $2 and then give up to any further action. Usually stronger than checking since at least we don't give free cards to any draw, and slightly lower the possibility of getting bluffed off the hand. A regular sized turn probe would generally be a mistake with this particular holding.

Id probably be looking at his 3bet stats. Vs a wider range I'd probably bet the turn. Vs a tighter range I might not. But generally a Btn 3bet vs CO open will pretty wide so I think we can profitably bet the turn. It's quite uncommon for villians to not cbet when 3betting and checked to which raises suspicions so id also be checking aggro stats. But generally I think a turn bet would be fine.