Question

why does visibility increase after rainfall

Answer 1

The main reason the visibility appear to improve after rain is that, often, when a rain happens is when a warm front associated with a low pressure, passes over us. Then it is followed by a cold front that brings polar air that is, relatively, dryer. Here is an example: at 15 C, a saturated cubic meter of air contains about 13 grams of moisture. At 0 C, it is down to 5 grams, hence a better visibility.