Without faith which is the case for a non christian, they will not connect that miracle with God, they will go down the reasonable route, and if there is not reason currently available then it would be a mystery.
A few examples
Psychological and Scientifically if one concentrates enough and believes he is getting burned, not only will he feel that pain of burning but he will experience those burns, this is a very rare case but it has been proven scientifically, without any real explanation.
In our Catholic faith we have seen the miracles of stigmata on various occasions. We connect this miracles with our faith, but for the unbeliever they will go the reason method only and will determine that it was psycholgical with physical outcomes.
In psycholgy there is the study of why no matter who we are, where we come from, that we can come up with the same exact stories over a period of time, for example many cultures in different times and cultures came up with a flood story, same thing for Adam and Eve Story, different stories, different characters same theme, even our stories come out of older stories. Now for the unbeliever they see this, study this and take the reason route alone and are convinced that the study of psycholgy alone is the truth, that we just come up with stories and they all relate, forgive me I forget what this is called. But for me and my faith, through this study, my faith is strengthened because there has to be an ultimate mover of this.