Probabilities from the periods there were six teams (non-logarithmic):
Montreal Canadiens: 0.001 (11 champs, 26 seasons)
Boston Bruins: 0.009 (26 seasons)
New York Rangers: 0.010 (25 seasons)
Toronto Maple Leafs: 0.014 (9 champs, 26 seasons)
Chicago Blackhawks: 0.052 (1 champ, 25 seasons)
Detroit Red Wings: 0.178 (5 champs, 25 seasons)
Montreal Maroons: 0.833 (1 season)
Ottawa Senators: 0.833 (1 season)
Hamilton Tigers: 0.833 (1 season)
The reason why NYR is so high on the list is due to the combinations with winning cause the chances to improve. But win too much like the Canadiens and the odds of winning overwhelm the combinations.
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The Colour Green
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