Generate probability function to determine values of individuals based on discrete CDF function

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The below figure reports a logarithmic cumulative distribution function of time durations in seconds. 68.14% of these durations lasted less than one minute, 96.28% for less than one hour, and 99.82% for less than one day.

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How can I create a probability distribution function using this graph of CDF values? I want to use that function in my simulation to determine the duration of individual nodes based on the probability distribution function.