Three Foggy Lookouts

A harbor master needs to know whether the strait is fogged in this morning before clearing a tanker to sail. Records show fog rolls in on exactly half of all mornings. She radios three lookouts posted along the strait. Independently, each lookout reports the true conditions with probability $\frac{2}{3}$ and reports the opposite with probability $\frac{1}{3}$. All three radio back: "fog." What is the probability the strait is actually foggy?