Consider two events $\mathrm{T}$ and $\mathrm{S}$. Let $\overline{\mathrm{T}}$ denote the complement of event $\mathrm{T}$. The probabilities associated with different events are given as follows: $\mathrm{P}({\mathrm{T}})=0.4$, $\mathrm{P}(\mathrm{S}|\mathrm{T})=0.3$, $\mathrm{P}(\mathrm{S}|\overline{\mathrm{T}})=0.6$. Find the conditional probability $\mathrm{P}(\mathrm{T}|\mathrm{S})$.