Use 'unlikeliness' when something has a low chance of happening, especially in formal or academic discussions. The unlikeliness of a snowstorm in July made it a poor research subject.
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Not Impossible
'Unlikeliness' implies a possibility, though small, rather than something that can't happen at all. Despite the unlikeliness of winning the lottery, many people still buy tickets.
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Negative Connotation
The term often suggests a skeptical or negative view of the potential for something to occur. The coach mentioned the unlikeliness of the team advancing, given their record.