I’ve learned that to calculate implied probability based on a gambling odds, you use the following formula:
Implied probability of win %= stake/ total payout
For example, if my fractional odds for team a to win are 5/1 (bet 1 dollar to win 5 dollars if team a wins), then the implied probability = 1/6.
Is there any intuition to why this is the case considering probability is the number of successful outcomes/ total number of outcomes?