An industrial safety system contains three independent gas sensors: A, B, and C. The probabilities that they correctly detect a leak when one occurs (sensitivities) are $0.9$, $0.8$, and $0.7$, respectively. The probability of a gas leak occurring is $0.1$. If there is no leak, each sensor has an identical false-alarm probability of $0.1$. If exactly two sensors trigger, what is the posterior probability that a gas leak is actually occurring?