Swinburne baldly states that there are no good deductive arguments for the existence of God. Kudos to him for the honesty to admit that.
He does think that there are good inductive (that is, probabilistic) arguments for God, and he thinks that collectively they make the case that the existence if God is more likely than his non-existence. But for each argument individually, he only makes the much weaker claim that the argument makes God's existence more likely than it would be without the argument.
He calls the latter type of argument a good C-inductive argument, and with a bit of Baysian analysis he shows that what you need in order to have a good C-inductive argument is
P(e/h,k) > P(e/~h,k),
e = the evidence under consideration,
h = the hypothesis, and
k = general background knowledge.
It is easy to come up with a good C-inductive argument for something that clearly isn't true. Take the tooth fairy, for instance. Let's let e be the evidence in favor of the tooth fairy's existence: all those coins that kids find under their pillows in place of teeth. And let's let h be the hypothesis that an invisible, non-human being exists who goes around replacing teeth with coins at night. And let's take k to be "mere tautological background evidence." (This is what Swinburne typically chooses for k.)
Now, it is clear that P(e/h,k) = 1. Because if the tooth fairy exists, then we will necessarily see the evidence e, for that is built into the very definition of the hypothesis h. And if the tooth fairy doesn't exist, well, then it might be true that kids will still find coins under their pillows (because their parents put them there), but it's not true of strict logical necessity, so we will have P(e/~h,k) < 1. So Swinburne's condition P(e/h,k) > P(e/~h,k) is fulfilled, and this is a good C-inductive argument for the tooth fairy.
None of this is to say that there's anything wrong with what Swinburne is saying here. It's just to point out what an extremely weak form of argument he's taking as the basis for his arguments for God.
A final comment on Swinburne's practice of taking k to be "mere tautological background evidence." By this he means only things that are tautologically true, like facts of logic and mathematics. By choosing this k, Swinburne makes it illegitimate to bring in any facts from our own experience about what sorts of entities actually exist in the world. In this way Swinburne turns what is usually an uncontroversial choice into a powerful tool in his favor.
To see how he employs this tool, let's jump to Appendix A where he replies to Mackie's critique. Mackie writes that
All our knowledge of intention-fulfillment is of embodied intentions....
and so "there is nothing in our background knowledge that makes it comprehensible" that God should be able to act directly in the universe to fulfill his intentions, as Swinburne claims he does.
Mackie has not taken seriously my intention ... to start without any factual background knowledge ... and so to judge the prior probability of theism solely by a priori considerations, namely, in effect, simplicity.
Now, if I were trying to convince someone that the Tooth Fairy doesn't exist, a large part of my argument would revolve around the complete lack of evidence that invisible, intelligent creatures exist. After all, arguing on the basis of past experience is the foundation of inductive reasoning. And how else to go about proving a negative?
According to Swinburne, we can't use this argument against (his argument for) God - simply because Swinburne has chosen a different set of background knowledge. Hmmm....