\begin{align} p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\ &=\frac{ \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) }{1+\frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) } \\ \intertext{\mathrm{suppose\ that} \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) \ll 1 } \\ &\approx \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) \\ &\propto \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) \end{align}