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I think of it this way and please correct me or add to this if you feel I'm mistaken. Given the ods of 1 to 4 of something occurring, then the probability is 1/5 or 20% from the definition above. To me '1 to 4' has always meant that out of five you have 1 chance of having 'it' occur. The denominator is the sum of all possible events.

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