Rede wrote:
....then it speaks of a truly astonishing power of the human mind light years beyond that with which we are familiar in day-to-day life.

Maybe in day to day life we use very little of the available brain power. I am not suggesting anything supernatural, just that whilst some of us are able to construct (for eg) amazing stories from nowhere, others may use that same faculty of imagination and call it precognition and/or prophesy. Many authors speak of their novels' plots coming to them as dreams, or visions. Sometimes they even state that they do not know the ending when they start a book. I am suggesting that the same type of creativity may be what causes some of us, in sleep, to construct plausible outcomes to events and happenings which later actually happen. If that is a 'probablistic' (had to look it up) prediction, is that a problem?