If the probability of rain tomorrow is 35%, then the probability of no rain tomorrow is 100% - 35% = 65%.
Think of it this way. It will either rain or not rain. There are no other options. Sure it might snow, but snow is not rain. When you consider probabilities, you need to think of all the options and the probabilities of all the option must add to 100%. In this case the options are rain and no rain, so the sum of their probabilities is 100%.