Why dont the electrical power lines trip when it rains if rain is a conductor of electricity?

Water is a very poor conductor of electricity and even if it has enough solutes in it to conduct electricity then it will still have a high resistance.

If rainwater were to conduct the electricity then that water would heat up and evaporate almost instantly.

But you need to remember that it would need a continuous channel of water to conduct electricity and the surface tension of water makes this unlikely to happen.

Overhead conductors are supported using insulators, the shape of which is designed to (a) shed water, and (b) to provide a long conducting path for any moisture between the top of the insulator and the bottom. For high-voltage lines, several insulators may be used in the form of 'strings', providing a sufficiently-long conducting path for any moisture path to have a sufficiently high resistance to prevent conduction.