It is based on Bayes' Theorem..
Here it is given that head will occur..But we dont know if it will be due to the regular or fake coin..
P(regular coin) = 2/3
P(fake coin) = 1/3
P(head | regular coin) = 1/2 [ As regular coin has one of two surfaces as head ]
P(head | fake coin) = 1 [ As fake coin has both surfaces as head ]
Hence
P(fake coin | head) = P(fake coin) * P(head | fake coin) / [ (P(fake coin) * P(head | fake coin)) + (P(regular coin) * P(head | regular coin) )
= 1/3 * 1 / [ 1/3 * 1 + 2/3 * 1/2 ]
= 1/2
Hence required probability = 1/2