• Uses the alignat env

\begin{equation} \begin{alignat*}{2} V_1 &\sim \text{Beta}(\alpha_1, \alpha_2 + \alpha_3 + \alpha_4), &\quad \rho_1 = V_1 \\ V_2 &\sim \text{Beta}(\alpha_2, \alpha_3 + \alpha_4), &\quad \rho_2 = (1 - V_1) V_2 \\ V_3 &\sim \text{Beta}(\alpha_3, \alpha_4), &\quad \rho_1 = (1 - V_1) (1 - V_2) V_3 \\ & \implies & \rho_4 = 1 - \overset{3}{\underset{k=1}{\sum}} \rho_k \end{alignat*} \end{equation}