The marauders' full moons have always followed approximately the same pattern. At least, certain stages of what was happening coincided every time.
Madam Pomfrey took Remus, to the Shrieking Shack through an underground passage originating under the roots of Whomping Willow, designed to keep his potential victims away from the werewolf.
And then potential victims made their way to the Shrieking Shack in the same way. It just so happened that they were doing this on a regular basis. We're talking about James, Peter and Sirius, who spent the nights of the full moon in the same house with a transformed werewolf.
This full moon also took place in the late autumn of the fifth year of Hogwarts. James and a nervous Sirius waited for Peter, already in rat form, to run past the striking willow branches and pull down the right twig at the roots with his teeth, after which the branches obediently fall off, making the tree a much more pleasant company, if only because it is not trying to play skittles with you. After that, three of them make their way through an underground passage to find themselves in a Shack with creaking wooden floorboards (they clearly show claw marks larger than wolf's), restless gray dust swirling in the air, an old and out-of-tune piano that appeared from nowhere and a sagging sofa with a blanket thrown over it, designed to provide at least a ghostly feeling of comfort in this environment.
And Remus, who had already turned into a wolf...
To meet the main course which had just crawled into an earthen passage under a willow tree, following a deer, a dog and a rat in the distance. Snape, advised by Sirius to get into the Shrieking shack, in person, almost nose-to-nose with a wolf.
A deer, a dog and a rat synchronously turn their animal heads at Snape, in the semi-darkness of a shack with boarded-up windows, their eyes glittered ominously. And a deep growl came from the wolf's throat as Snape instinctively backed away, grabbing his wand.
Human. Sounds yummy.