\begin{equation*}
    \mathbf{P}(\Delta p_A = -\frac1N) = p_A \cdot \sum_{k_A+k_B+k_S = k}\frac{k!}{k_A! k_B! k_S!} q_{A|A}^{k_A} q_{B|A}^{k_B} q_{S|A}^{k_S} \cdot \frac{k_Bg_B}{k_A g_A + k_B g_B + k_S g_S}
\end{equation*}
