 Upper limits based on the CLs method were used in numerous publications of experimental results obtained at particle accelerator experiments such as LEP, the Tevatron and the LHC, most notable in the searches for new particles.The original motivation for CLs was based on a conditional probability calculation suggested by physicist G. Zech for an event counting experiment.Suppose an experiment consists of measuring formula_24 events coming from signal and background processes, both described by Poisson distributions with respective rates formula_25 and formula_26, namely formula_27.