First, it is simply not true that we have an experience of the non-existence of miracles. The non-existence or non-occurrence of anything is never a matter of experience, because non-existence cannot ever be experienced. All experiences are positive in this sense. What the majority does have is the experience of never witnessing miracles. But the experience of never witnessing miracles is not the same as the experience of the non-existence of miracles. So a cumulative or probable case against the existence of miraculous events cannot be made simply from experience. All that can be said is that most people have not witnessed miracles, and to this the theist wholeheartedly agrees.
But even here one must be reserved about building a probable case for “not-witnessing” miracles. This is because any experience of not-witnessing miracles needs to be relevant. A simple unqualified “not-witnessing” of something proves nothing. For example, suppose a man were on trial for murder and the prosecutor says, “I have ten witnesses that saw this man commit the murder.” The defense attorney says in response, “Well that’s nothing, I can provide over 500 witnesses that did not see him commit the murder” (indicating anyone who was not there at the scene at all)! But clearly there is something wrong here with the defenses’ response. It is not merely just an overall “not-witnessing” that is important but rather the witness for or against an event should be relevant in some way to the issue at hand. Relevant witnesses would have to have been there, looking in the right direction, etc.
(Both of these above points come from my conversations with Christopher Martin of the University of St Thomas.)