Learn Turkish: Hava berbat, karın duracağı yok. - The weather is awful, the snow has no intention of stopping.

This sentence uses the lesson's target structure for showing a lack of intention or sign of something happening: Verb + -(y)AcAk + possessive + yok. Literally, it means "the snow's future stopping does not exist." It is a very natural way to express that an event shows absolutely no sign of happening anytime soon.

Why does kar (snow) take the genitive suffix -ın here?

Because the nominalized verb (duracağı) acts like a possessed noun. To say "the snow's stopping," you need to link the subject (kar) to the action using the genitive case. So, karın ("the snow's") pairs with duracağı ("its future stopping").

Is it normal to use this "intention" structure for inanimate objects like the weather?

Yes, absolutely! When used with people, this structure usually means a lack of intention, like onun geleceği yok (he has no intention of coming). When applied to inanimate things or forces of nature like the snow, it translates better as "shows no sign of" or "doesn't look like it will."

What is the difference in feeling between saying kar durmayacak and karın duracağı yok?