You'll have the trail all to yourself
The rain empties the trails, so you may not meet anyone and be able to enjoy your hike with a feeling of real exclusivity and tranquillity. A little silence and lots of patience may enable you to meet animals you don't usually see.
However, make sure you're clued up with the signs and map and compass reading as you may not come across any other hikers if you get lost. Also, always tell someone you're going hiking, telling them where and for how long.