People 'confess' to things they didn't do every once in a while, too. Remember that guy who tried to confess to the murder of the child beauty queen around five years ago, but it turned out the semen on the body wasn't his?
In a photograph of a person drinking underage, there is evidence because there is a picture. In a murder case, there is a body somewhere.
If I try confessing to somebody's murder, but nobody knows where the body (or even the crime scene) is, the Crown won't prosecute me because its a waste of his time.
There's a difference between being prosecuted and being convicted, incidentally. District Attorneys (I call them Crown Attorneys a lot, because I am Canadian, and they work for the government and by extension the British monarchy. We call government owned corporations Crown Corporations, too) decide what they do and don't try to prosecute. If a jury (the people who get to make the verdict in criminal court, not the judge) can't figure out what you did, it will look bad for the CA/DA who wasted money trying to charge you.
Why is this in the Confessions thread, anyways?
EDIT: In Mullen's case, the police will now be able to connect him to premeditated murder through his 'confession', because there are two bodies.
But if I say
Hey, everybody, I killed John Lennon
I won't be prosecuted or convicted, because it is clear I could not have done so.