A boutique hotel has three types of rooms: Economy ($E$), Deluxe ($D$), and Suite ($S$), representing $50\%$, $30\%$, and $20\%$ of total capacity respectively. The probability of a guest requesting room service is $0.1$ for $E$, $0.3$ for $D$, and $0.6$ for $S$. If a guest is observed requesting room service, what is the probability they are staying in an Economy room?