Positivity of posterior variance

Question

Given a gaussian process with a kernel k, we know the posterior variance after conditioning on data $D_n = \{x_1, \cdots, x_n\}$ is given by $$ k(x,x) - k_n^T(x) K_{nn}^{-1}k_n(x), $$ where $k_n(x) = (k(x, x_1), \cdots, k(x, x_n))^T$ and $({K_{nn}})_{i,j} = k(x_i, x_j)$. How can one immediately see that $$ k(x,x) \ge k_n^T(x) K_{nn}^{-1}k_n(x)? $$