On win markets the reduction factor is applied to the total odds. Thus, if a reduction factor of 12% is applied to odds of 5, the resulting reduced odds would be 5 - (12% x 5) = 4.4. In this case, it is mathematically provable that the reduction factors must sum to 100%, if they are to be fair.
However, for place markets, the reduction factors are applied to the odds minus the stakes (i.e. the odds-1) so that if a 40% RF is applied to a bet at odds of 3, it gets reduced to 3 - ((3-1)*40%) = 2.2. In this case, the sum of the reduction factors do not sum to 100%, or any specific value.
The calculation to get these reduction factors is based on predicted odds (from a reputable source such as the Racing Post) and uses an iterative process to calculate the 'fair' reduction factor based on the effect of removing each of the runners in turn. In other words, it removes a runner and calculates what the reduction factor would have to be in order to return a 'fair' market back to 100%, after the removal. For this purpose a 'fair' market is assumed to be one where the market reflects the reduction factors precisely.