WAIT......Who is excluding all natural explanations??? We consider all explanations natural and supernatural when considering likelihood.
The OP is, for one. The OP dismissed all natural causes as so unlikely that they could be disregarded. Any time we conclude a supernatural explanation without considering the relative probability of the possible explanations - which MUST include consideration of the likelihood of the supernatural explanation - we're excluding all natural causes.
You know that line from Sherlock Holmes that goes "when you eliminate the impossible, then whatever remains, however unlikely, must be the truth"? It only works when the things being eliminated are actually impossible, not merely unlikely. When we conclude that some explanation must be true because it's the only one left, then we're implicitly saying that all the other explanations are impossible... not merely improbable, but impossible.
Now we're on the same track.
Millions of events in the history of mankind is evidence for consideration in our likelihood deliberation.
IOW, bad evidence becomes good evidence if you have enough of it.
Edit: regardless, what do "millions of events in the history of mankind" have to say about this story? Even if supernatural forces exist, we still have natural explanations. People do win lotteries by chance. Lotteries have been rigged. People do sometimes lie.