Alice is learning more advanced techniques for the shift cipher. She now chooses a random five$-$letter word $($so all five$-$letter words in the dictionary have the same probability$)$ and encrypts it using a shift cipher with a randomly chosen key $($that is$,$ each possible shift has probability $1/26).$ Eve intercepts the ciphertext evire. Show that

$P(M=$ arena $|C=$ evire $)=\frac{1}{2}$