If there is evidence of the possibility that an event will occur, is there a finite probability that the event will occur?
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I think you are assuming the answer straight from your question- if there is the possibility that an event will occur, then that exact possibility holds some probability of the event occurring- because how else would you know it is possible?
For example, the converse- if you said there is no possibility for something, then there's no probability of it happening. It's just a vague formulation for the same thing.