Question: Mean Reversion

I found on the internet a basic definition of mean reversion ( http://mathworld.wolfram.com/ReversiontotheMean.html )

I would assume such definition would also work as an definition of stationarity:
 

" Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater the probability that the next measured variate will deviate less far. In other words, an extreme event is likely to be followed by a less extreme event."

How can I prove mathematically with density functions that "the greater the deviation of a random variate from its mean,

the greater the probability that the next measured variate will deviate less far"  ...?