Upon reflection I agree with most of your post, but to answer your question
Why then in the case of cancer does the fact that it can be explained suddenly make it less of a miracle? It is still equally as improbable, whether explainable or not.
Going by my definition (which after reading your post, I can admit the flaws), the fact that a situation can be explained does not change the probability, but to me eliminates the exceptional circumstances. If the doctor said “X caused Y to change so we could treat the cancer with Z”, as apposed to “ Well we treated the cancer with Z and it suddenly disappeared”, the the former seems a lot less miraculous.
What does whether time is infinite or not have to do with the miraculous/non-miraculous nature of an event happening here and now?
My statement “I suppose it depends on your view on time... Is it infinite?” was in response to this from Phat:
Is everything in life bound to happen eventually according to the laws of statistical improbability and probability?
The probability of something happening depends on the number of trials an event has had. If a dice was thrown every minute for the rest of time if it was infinite, a six is infinitely more likely to occur eventually than if time was finite, as there would be a limited number of rolls and always the possibility of a six not being rolled in that finite time.
So if you believe time goes on forever, the chances of everything in life being bound to happen are infinitely greater than if time was finite, and there was only a number of finite situations.