There are two cards missing from a deck. Two cards drawn are found to be spades, what is the probability the missing cards are spades?

Question

I have tried the following two methods: 1) Found the probability of drawing two spades in each case of 2 spades misssing, 1 spade missing and no spade missing and then used Bayes Theorem

2) Found probability of selecting two spades from a deck from where we have already drawn two spades.

In both the cases I get my answer as 11/245, however the book where the question is given says the answer is 23/206.

Can anyone guide me to my mistake please, any help is appreciated.

Answer 1

Essentially the question has been answered, correctly, by the asker and in the many comments. Namely, the book is wrong, and the probability is $\frac{11}{245}$. This is my answer too, but it would be redundant to explain it now.