Actually I was trying to express that the birthday paradox does not apply when you to find a plaintext that evaluates to a known hash, as you'd need to do for password cracking or forging a signed email for example[1]. The birthday paradox only gives you the probability that of a random set of hashes, two are the same. It's "if I generate n random pieces of plaintext, how big is the chance that two of them generate the same hash." Actually it gives you the probability of picking the same element twice from a finite set of elements when you pick n times.

[1] When generating emails more restrictions apply: The colliding plaintexts have to be at least somewhat coherent and probably should express something the attacker wants to express.

Edit: Forgot a negation in a crucial place. Darn.