You Can't Disprove a Miracle

[SteveII]

Using the same example above, are eyewitness accounts of the event, timing, and context sufficient to increase the probability of an event having a supernatural cause versus a natural one?

You're still arguing that low probability events equal miracles.  No they don't.  Low probability events equal low probability events.  The probability cannot demonstrate that it has a supernatural cause, only evidence of an actual supernatural cause can do that.  Eyewitness accounts to unexplained events, even if held to be reliable, even given certain context, do not show the supernatural.

Click here for a Wikipedia article on Bayesian inference and probability theory.  Probability theory says that you not just assess the probability of an event and make your conclusion, but you must update that probability given any new evidence, information or conditions (timing, context, etc.). 

"The posterior probability of a hypothesis is determined by a combination of the inherent likeliness of a hypothesis (the prior) and the compatibility of the observed evidence with the hypothesis (the likelihood)."

You can run the formula for each hypothesis (H) and compare.Let's do the crippled man:

                    P(E/H) x P(H)
P(H/E) = ------------------------------
                          P(E)

H = Hypothesis, man was healed by Jesus
E = man walks, including timing and context

P(E/H) - probability of E given the hypothesis that Jesus can heal = .90
P(H) - probability that Jesus can heal cripple before E was observed = .01
P(E) - likelihood that E happened without H (call it "natural causes") = .05

             .9 x .01
18% = ----------------
               .05