Mixture distributions [2* P]

Consider a density model given by a mixture distribution

$$p({\bf x}) = \sum_{k=1}^K \pi_k p({\bf x}\vert k)$$ (9)

and suppose that we partition the vector ${\bf x}$ into two parts so that ${\bf x} = ({\bf x}_a, {\bf x}_b)$ . Show that the conditional density $p({\bf x}_b\vert{\bf x}_a)$ is itself a mixture distribution and find expressions for the mixing coefficients and for the component densities.