Take the working lamp to all the sockets and make sure they are all good. Take all three failing lamps to the working socket and work on one at a time. Verify that they don't work. Use the good lamp (bulb) and if it does not light verify it's still good by testing it again it in the working table lamp. If the lamp holders have switches they are fiddly little things that often fall to bits - new ones can be bought from specialist shops.
The lamp holder, switch, plug connections, fuse in the plug, cable connections to the bulb holder can all be examined taking great care not to electrocute yourself.
Connectors in the lamp holder to the bulb are often difficult to diagnose. With the lamps UNPLUGGED (on a bayonet connector BC) make sure that the spring loaded connector pins are both the same height and you can feel the spring tension. On a screw connector (ES) use a small screwdriver to pull the centre contact up a fraction.
If by now you have not found the problem(s) either your table lamps are haunted or you have overlooked something.
Peccavi, November 2008
