In the story, Professor Snape (and we assume from here on out that you're imagining Alan Rickman, who played him in the movies) is suffering from existential despair, despite having a sweet teaching job in a smelly dungeon and enviably greasy hair. He brings his troubles to his superior, Dumbledore, who orders Snape to take a vacation in the sunny land of the Teletubbies. Snape does just that.
"Jesus, I meant stay home and watch TV, what's wrong with you?"
Now that the writer has properly established a plausible scenario for the characters to meet, let the f*****g begin.
Where It Gets Really Creepy:
It turns out the Teletubbies are slightly curious about sex, and who better to teach them about it than a potions professor at a magic school? Snape demonstrates how it's done with female Teletubbie Laa-Laa:
"Teletubbies, lay her with me, I'll teach you how to be a man. Oh, but you Poo, aren't ready yet. You are too young baby. Stay here in the corner and play with you small hose."
So Laa-Laa is ripe for f*****g, but Po is out of the question, because that would be weird.