Kan complexes and maps of simplicial sets seen as path

I'm trying to solve the following exercise:

Let $\lambda: \Delta [1]\to K$ be be a map of simplicial sets (which we can think of as a path) where K is a Kan complex. Prove there exists a path $\lambda^{-1}: \Delta [1]\to K$ such that $\lambda^{-1}(0)=\lambda(1)$ and $\lambda^{-1}(1)=\lambda(0)$.

I don't understand how we can see $\lambda: \Delta [1]\to K$ as a path. And more generally, it seems that to understand a map of simplicial object, we only have to look at non-degenerate element, I think it has something to do with the simplicial identities but again , I tried to do some computation to see why but I wasn't succesful. Can someone help me to understand simplicial maps ?