The first thing to do, would be to specify a velocity component for the raindrop class; which specifies how fast the raindrop falls. To apply this, try the following (assuming the velocity component is called yVelocity):
// Take this line
raindrop.y -= 200 * Gdx.graphics.getDeltaTime();
// Replace with something like
raindrop.y -= raindrop.yVelocity * Gdx.graphics.getDeltaTime();
You can set the yVelocity in the constructor of the raindrop using the random function. (See here for an example of how to use the random function to get a value within a range).
If you want only specific random raindrops to have a random speed applied to then; use the random function to determine whether the constructed raindrop is allowed to have a random speed applied, by checking that the random value falls within a certain range.
The following example applies a random velocity to roughly 1 in 10 raindrops.
if (Math.random() >= 0.9) {
raindrop.yVelocity = //Random velocity calculation here;
}
else {
raindrop.yVelocity = 200;
}
To have the raindrops move faster as they travel down the screen, simply increase yVelocity by a gravitational constant in the update call for each raindrop. :)
EDIT: I would recommend that you made Raindrop a class of it's own, as using rectangle directly in that fashion severely restricts what properties you can apply to the raindrops.