As far as I remember the mathematical concept odds is defined as:
the probability something is true divided by the probability that it is not.
Or as Wikipedia puts it:
the ratio of the probability that the event will happen to the probability that the event will not happen.
However, reading about odds in sports gambling, Wikipedia says this:
In gambling, odds represent the ratio between the amounts staked by parties to a wager or bet. Thus, odds of 6 to 1 mean the first party (normally a bookmaker) stakes six times the amount staked by the second party.
Which implies that assuming the bet is fair that the quoted "odds" are actually $\frac{1}{P(E)}$ where $E$ is the event you are betting on. This understanding is confirmed by an answer on stats.stackexchange (which doesn't assume fairness).
The odds you have are in decimal format, which the bookmaker calculates as:
$$ d_E = \frac{1}{p_E + o_E} $$
where $d_E$ is the decimal odds for event $E$, $p_E$ is the bookmakers estimated probability of event $E$, and $o_E$ is the over-round which the bookmaker adds to the decimal odds for event $E$.
So even assuming $o = 0$ for all the $o$'s, then the bookmakers odds aren't really "odds" in the sense of $\frac{P(E)}{P(\neg E)}$ but instead $\dfrac{1}{P(E) }$. Thus the word odds is going around with more than one meaning. Correct?