Water, in its purity, does not conduct electricity. As distillation is a purifying process, the water produced from it is rather pure. As a result it does not conduct electricity. Rain water, however, is a rather diverse mixture of different substances. Its conductivity primarily comes from the different inorganic salt soluted in the rain water. 
Rain water does not conduct electricity because it is the purest form of Water which is about 80 to 95% pure...
It does not conduct electricity because no exchange of ions take place...
rain water doesnot conduct electricity since its the purest form water