You guessed it, transparency is involved. But it isn't as simple as all that.

1. Your transparency map should, ideally, be more opaque where there are multiple layers of cloth, such as seams, collars, cuffs etc.
2. Not all colors become transparent at the same rate. If a character was wearing an outfit with a white background with a darker pattern, the pattern should be less transparent. Also, most colors darken when wet, so you probably want to change your base texture as well.
3. Wet cloth is often shiny, so you want to add some reflectivity in the material room to fabrics such as polyester and denim.
4. Wet fabric drapes differently. It tends to be both heavier (so it hangs lower), and also stickier. You might try using the cloth room and playing around with the parameters.