\begin{align} p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\ &=\frac{ \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } }{1+\frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \\ &\approx \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \\ &\propto e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \\ \end{align}