How does a probe screwdriver work?

You might get an intelligent answer if you describe what you are talking about.

SCREWDRIVER / VOLTAGE TESTER like this

There is a high resistance resistor (limits current through the device to safe sub-milliamprere level maximum) and a neon bulb (lights at very low current). The circuit is the same as used on neon lamp indicator lights found on switches etc.. only difference being that the current limiting resistor has higher resistance (lower current) and safer design (will not arc over or fail on any normal use or overvoltages).

When the tip is connected to live wire (or is near it so that there is enough current through capacitance) there is a small current that flows to your body to ground and makes the neon bulb to put out some light. If you are touching ground with other hand, the maximum current flows through your body (limited to safe value with the current limiting resistor). If you are not toucvhing ground the current flows to ground through the capacitance between your body and ground (still enough current

This kind voltage tester can fail in case you are very well insulated away from ground sources. In that case there is not enough "leakage" through you that the would make the neon bulb to flow.

Information on neon bulbs: