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\begin{equation} P_{jc} = \frac{ \mathrm{exp} \left( \betaVec' \xVec_{j} - \alpha p_{j} \right) } { \sum\limits_{k \in \mathcal{J}c}\mathrm{exp} \left( \betaVec' \xVec{k} - \alpha p_{k} \right) }, \quad\quad \forall c \in \left {1,2,3,\dots C \right }, \quad j \in \mathcal{J}_c, \label{eq:logitProbability} \end{equation}
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