The best reference on probability transformations I know is:

Graham VA, Hollands KGT, Unny TE (1988) “A time series model for Kt with application to global synthetic weather generation”, Solar Energy, 40 (2), 83-92

Section 2 of that paper covers probability transformations.  I can give you a rough description though.

A probability transformation is essentially the process by which a professor grades students "on the curve".  Say you have a data sequence with some distribution, and you want to transform those data to conform to a different distribution.  You start by calculating the cumulative distribution function (CDF) of the original data, then go through the data points one by one.  For each data element, you calculate its percentile by referring to the CDF of the original data sequence.  Say the first value is 6.5 and its percentile is 75%, meaning that it exceeds the value of 75% of the values in the original data sequence.  Then you look at the desired CDF and see that the value of the 75th percentile is 40.  So you change that first value from 6.5 to 40.  If you do that for every element, the CDF of the transformed data set will be exactly what you asked for.