The “gene effect” file contains the corrected CERES scores, which measure the effect size of knocking out a gene, normalized against the distributions of non-essential and pan-essential genes. The probabilities assess, given a gene score, how likely to be a member of the non-essential distribution or the common essential distribution in that cell line. The key difference between using a fixed threshold on CERES score and a threshold on the probabilities is that the probabilities take into account the screening quality, which varies from line to line.
So which one should I use?
Depending on the question you want to ask, you may want to choose to use one measure or the other. For cases where you are interested in potentially subtle variation in the strength of killing, such as computing co-dependency correlations, using the CERES scores makes sense. However, if you are only interested in binary relationships of which lines are killed or not, for example, when looking for biomarkers which classify lines into sensitive or insensitive, then the dependency probabilities may make more sense to use.