GATE DA 2024 Q58: P(T | S) by Bayes' theorem

Consider two events $T$ and $S$. Let $\overline{T}$ denote the complement of the event $T$. The probability associated with different events are given as follows:

$$P(\overline{T}) = 0.6, \quad P(S \mid T) = 0.3, \quad P(S \mid \overline{T}) = 0.6$$

Then, $P(T \mid S)$ is ______ (rounded off to two decimal places).