The probability of rain rather than drizzle increases with thicker clouds because thicker clouds contain more moisture and have a greater vertical extent, which allows for more significant condensation and droplet formation. In thicker clouds, the updrafts can support the growth of larger droplets, making it more likely that they will coalesce and fall as rain rather than evaporating as drizzle. Additionally, thicker clouds often indicate more robust weather systems, which are conducive to heavier precipitation.