There are times in our lives when the ‘sensible’ explanation is just not probable or even possible. Things occur that are simply beyond probability, beyond mere coincidence. We could invoke the apocryphal statement attributed to Freud, “sometimes a cigar is just a cigar,” but it explains nothing.
However, just because we have experiences that defy the odds, it does not mean that they are super-natural. Everything that is, is natural. We may not understand the mechanism for the manifestation of all phenomena and experiences, but there is one… and it is not magic.
The mechanism is always action and consequence, cause and effect: it is karma. Sometimes, the complexity of the interaction between multiple causes and conditions is beyond our capacity to understand, but everything that happens is ―in essence― just that: the coming together of causes and conditions.