The answer is the second one.
Here we're using conditional probability.
The event that we saw was the cipher text.
That's the encryption of m.
What we want to know whether the message is equal to m.
Both of those are drawn from the set of all possible messages.
In order for the attacker to know nothing is the same as the probability that the message is m
without knowing the cipher text.
The first answer would be correct if, a priori, the attacker knew nothing about the messages.
All the attacker knows is each message is equally likely.
In that case, the probability that the message is m
would be 1 over the number of possible messages not depending on the cipher text.
The problem is the attacker might know something more.
They might know that some messages are more likely than others.
In most realistic scenarios this is the case.
The attacker knows that the message is likely to be a valid sentence in English.
Very few possible bit sequences correspond to that, so all messages are not equally likely.
That's why choice 1 is not the definition we want.
We want choice 2 where whatever the attacker already knew about
the probability of the message as m is not affected in any way by seeing the cipher text.
That's our definition of a perfect cipher.
Now the question is can we prove that the one-time pad has this property.
