No compression on three cylinders

Rings wouldn't drop it to zero unless they scored the cylinder walls with some heavy gouges. I would suspect valves as the 4.7 is like it's baby brother the 3.7 in liking to have valve failures in some years. An easy way to tell would be to get one of the cheaper bore scopes that hook to a phone, tablet or computer and use it to look inside the cylinders through the spark plug holes. Some parts stores have them as loner tools but make sure they have the smallest camera head. Another way would be to do a leak-down test and listen for the air leaking past the various parts. If your compression tester is a thread in type with a quick disconnect you can use it for the testing. Just remove the schrader valve from the hose and use air from a compressor with each of the "bad" cylinders on compression TDC and the crankshaft held in place, It only takes about 10-20 psi to hear leakage. I think you will find the leakage is from the valves. From there I would remove the valve covers and check the valve spring heights at the top of the valve retainer. Loose seats or springs will show up easily there. From there it becomes a choice of how to proceed.

Let us know what you find and we can go from there.