#1 is the standard way to say this. In #1, "rain" is a noun. However, #2 is absolutely correct. I can see no reason why #2 would be incorrect. In that case, "raining" would be used as a gerund, a noun, so the structure of sentence #2 is exactly the same as the structure of sentence #1. If you want to use "raining", it sounds more natural if you use it as an adjective (predicate complement): "there is a high probability that it will be raining tomorrow".

#1

The correct answer is "There is a high probability of rain tomorrow".