His argument, repeated in different contexts, is essentially this. If God did not exist, life, the universe, and everything in it (including our minds) would look just the way they do. But if God exists, He could have created life, the universe, and everything in innumerable ways and, Carrier conjectures, surely not in the fractured, imperfect, pain-guaranteeing way we see. Therefore, because “the probability that a ‘designing’ god exists but never intelligently designed anything is likewise virtually zero, since by definition that’s also not how such a god behaves” and for other reasons Carrier creates, it is likely God does not exist.
Not only is Briggs' analysis helpful, you can also get a feel for how Bayesian probability is supposed to work. All in all, it's best to read the whole thing.
We all think from time to time something on the order of "if I were God ...". This is especially true when we face some of the tragedies and horrors and apparent unfairness of life. But, if, as I believe, God does exist, He has perfect knowledge, something that is simply incomprehensible and unimaginable to us. If a person doesn't want to believe in God, there's nothing much I can do to convince them. It's a choice. I think there is evidence that God exists; they do not find that evidence compelling. Nevertheless many are willing to believe in chance. Briggs, again:
He appears to believe, like many, that evolution occurs “randomly” and is a “product of chance”. That’s impossible. Nothing is caused by “chance” or occurs “randomly” because chance is not a cause and neither is randomness. Chance and randomness are measures of our ignorance of causes, and are not themselves ontological realities.