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I think the trick would be how you define 'similar'. If you have an infinite number of possible outcomes, the probability of any one of them is essentially zero. But if you take a 'large enough' group of them by also including similar outcomes, you might be something nonzero. For example, take a probability distribution that looks like a bell curve. The probability of any given value occurring is 0 (the area under the curve is 0, since it's an area under a single point). But the probability of a given value or /similar/ values occurring is nonzero if you think of the similar values as forming an interval around the original given value. So, the area under the curve is nonzero because it's an area under an interval.
/math
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