Does anyone have any explanation at all as to how it's possible to alter probability on a macroscopic level?
Nope. Which is why I think the concept behind "Rivals" is actually one of the best pieces of science fiction in DS9 if not in the entire history of Star Trek.
Face it, modern science and philosophy is at complete loss to even begin to explain the nature of "chance" or "probability". The human mind cannot comprehend the concept, not in the sense we comprehend things like F=ma or E=mcc or 1-1=0 that have their direct counterparts in the sticks-and-stones world we apes have always lived in. The brightest minds in natural sciences and mathematics resort to meaningless handwaving, at best managing to create a descriptive model rather than an analytical one. The best philosophers only manage to discuss the effects of randomness (or of denying it), rather than attack the root causes.
We don't know what probability is, or how it behaves in atypical conditions - unlike the case with many other natural forces, such as electromagnetic interaction whose scaleability we have already studied and modeled from the very small to the universe-wide, at times determining stunningly good, umpteen-decimal predictive values for phenomena that are actually studied only decades after the prediction. Instinctually, we feel the need to see probability as something similar to this EM interaction or like phenomena - we feel an explanation lies somewhere deep down, waiting to be discovered so that the world makes sense to our monkey brains once again. A lot of the arbitrariness of nature has been made less arbitrary by giving it "scientific explanations". The basic phenomenon of probability still utterly lacks such an explanation.
"Rivals" may not be the most thorough philosophical discussion on the subject, or the most detailed technological analysis. Nor is it a particularly enjoyable episode of Star Trek drama. But the concept it brings up is perfectly valid and the questions arising on the role of randomness in the macroscopic world are worth asking.
Timo Saloniemi