The probability of God not existing given background knowledge can be zero only if the conjunction of God's non-existence and background knowledge is necessarily false.

The first conclusion, then, is that the probability that God exists is lower given the combination of \(P\) together with our background knowledge than it is given our background knowledge alone. Thus \(P\) disconfirms \(G\) in the sense of lowering the probability of \(G\). The second conclusion is that \(P\) disconfirms \(G\) in a different sense—namely, it, together with our background knowledge, makes it more likely than not that \(G\) is false.