Say you have one continuous variable X, and one discrete variable Y, and you desire to express the probability of X conditioned upon Y using a gaussian model:
\begin{equation} p(x|y) = \begin{cases} \mathcal{N}(x \mid \mu_{1}, \sigma_{1}^{2}), y^{1} \\ \dots \\ \mathcal{N}(x \mid \mu_{1}, \sigma_{1}^{2}), y^{n} \\ \end{cases} \end{equation}