In English the word "odds" is used in many ways;
Mathematically, the probability of an event A is a number between 0 and 1, while the odds of event A is the probability of event A divided by the probability of not-A. This distinction between odds and probability is not always clear in non-technical English, as the interpretation is often
odds of A is 3 to 1 => probability of A is 1/(1+3)=1/4
odds of A is 1 in 3 => probability of A is 1/3
To make things even more confusing, in sport bettings they use the convention
odds of Liverpool winning is 4.0 => probability of Liverpool winning is 1/4
To my knowledge and after some searching, I believe there is no word in Esperanto for "odds" as a mathematical term. Therefore, I suggest that your translations should be explicit
For the phrase "The odds are 3 to 1" I would write
La probablo/probablece de tio estas 3obla pli granda ol de la mala.
or avoid the odds altogether by writing
La probablo/probableco estas 1/4
Likewise "The odds are one in a million"
La probablo estas 1/1,000,000.
For "Current odds: 203 on Hank, 341 on Mike", I would write
Nuna repagkvanto: 203-obla por Hank, 341-obla por Mike