"Implied" Probability?

What is the difference between odds and probability? Why is 1:1 odds
equal to a probability of 1/2?
I plan on being a bookmaker, and I need to know whether the implied
probability of these odds will be greater than 1 so I can make a
profit:

Home team wins: 1:4
Visiting team wins: 1:1
Tie: 1:9

What is "implied probability"?

Thanks!!!!!

.

Relevant Pages

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