Spoiler: SNAPE FUCKS TINKY WINKY.
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 fucking 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."