An autonomous drone navigation system relies on two sensors, $S_1$ and $S_2$, that detect obstacles independently. $S_1$ has a failure rate of $15\%$ and $S_2$ has a failure rate of $25\%$. The system triggers an emergency stop if at least one sensor detects an obstacle. Given that the emergency stop has triggered, what is the probability that $S_1$ failed to detect the obstacle?