A letter is known to have come from CHENNAI, JAIPUR, NAINITAL, MUMBAI. On the postmark only the two consecutive letters AI are legible. The probability that it came from MUMBAI is $\frac{k}{m}$where k,m are coprime then the value of ‘k+m’ is

$A_1:$Selecting a pair of consecutive letters from the word CHENNAI

$A_2:$Selecting a pair of consecutive letters from the word JAIPUR

$A_3:$Selecting a pair of consecutive letters from the word NAINITAL

$A_4:$Selecting a pair of consecutive letters from the word MUMBAI

$E:$Selecting a pair of consecutive letters from the word AI

Required probability $=P\left(\frac{A_1}{E}\right)=\frac{\frac{1}{5}}{\frac{1}{6}+\frac{1}{5}+\frac{1}{7}+\frac{1}{5}}=\frac{42}{149}$