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[en] Highlights: • The scope is to find the relationship among SO probabilities, Z and electron density. • A scaling law is suggested, allowing us to find the SO probabilities for atoms. • SO probabilities have been scaled as a function of target Z and polarizability. - Abstract: The main scope in this work has been upon the relationship between shake-off probabilities, target atomic number and electron density. By comparing the saturation values of measured double-to-single photoionization ratios from the literature, a simple scaling law has been found, which allows us to predict the shake-off probabilities for several elements up to Z = 54 within a factor 2. The electron shake-off probabilities accompanying valence shell photoionization have been scaled as a function of the target atomic number, Z, and polarizability, α. This behavior is in qualitative agreement with the experimental results.