The Christian believer can respond in two ways to this argument.
On a first note extraordinary claims do not require extraordinary evidence, rather they require sufficient evidence. An extraordinary claim may very well be the best explanation for a set of data and if so it would be silly to deny it.
A second point concerns probability theory. Now, the Christian is aware that this argument is often made against the resurrection of Jesus. Essentially the skeptic would argue that the evidence for the resurrection is not “extraordinary” enough to grant the conclusion that there was a miracle. But there is a response to be had here.
Apologists routinely point out that Jesus’ resurrection is best explained by a set of facts known as the minimal facts. The minimal facts approach only considers historical data that the majority of scholars accept. There are four of them, namely, that -1- Jesus died via crucifixion, -2- that he was buried, -3- that three days later the tomb Jesus was placed in was found empty, and -4- that the disciples, the persecutor Paul, the doubting brother James, and others had post-mortem experiences of the resurrected Jesus.
Now, if we were to apply probability theory to these four basic facts we would need to then ask “What would the probability be of the resurrection not happening in hindsight of these four facts?” To which philosopher William Craig answers: “It is highly, highly, highly, improbable that we should have that evidence [four facts] if the resurrection had not occurred” (1).
1. Craig, W. 2012. Stephen Law on the Non-existence of Jesus of Nazareth. Available.