Markov Chain Mixing Time of the Complete Graph

Question

I'm having a hard time understanding mixing time for Markov Chains on Complete Graphs (Kn).

We can define the probability matrix for Kn where Pi,j=probability of going from i to j (technically 1/degree(vi). This is assuming the edges have no weights and there are no self-loops.

Also, the stationary distribution pi exists such that pi*P=pi.

For the complete graph, pi can be defined as a 1xn vector where each element equals 1/(n-1). I got this from defining each element to be deg(vi)/sum(deg(N(vi))) - the degree of node i divided by the sum of the degrees of its neighbors.

What would be the mixing time? I'm not sure how to go about finding it.