You are playing in a NT contract and the lead is a low spot card. That suit on dummy has:
J9x and you hold Ax in your hand. The correct percentage play is the nine. Statistically, LHO is more likely to have led from K10xx(x) OR Q10xx(x) than from KQxx(x). On a good day, the 9 forces a ˝ of the royal marriage on your right. You kill the sovereign with your Ace and dummy's Jx remains a second stopper in the suit.
If you do NOT own the nine, your only chance is to fly with the Jack of the suit, hoping LHO has led from KQxx(x). (An exception would be if you think RHO is VERY inexperienced and might put in the King or Queen from K10x or Q10x or K9x or Q9x. In that case, you can try a low card, but the odds are against you. If LHO had either high honor with BOTH the 10 and the nine, would not have led a low spot card—would have led 10 in standard leads or 9 in “jack denies” leads.)
Against a suit contract, flying with the Jack is hopeless as LHO will NOT be leading low from KQxx(s) against a suit, so play low and hope for an error by RHO.
Another combination: you are again in NT and have AKJ8x opposite 32 in dummy with NO chance to ever get to dummy for any finessing. Play FROM THE TOP! Do NOT play the Jack when you do not own the ten. Do not squander the eight. Your best hope is that the suit divides 3-3, but you will also get four tricks IF either opponent has Q9 or Q10 doubleton (as your 8 gets promoted).