'The odds' are just one way of expressing the chance, or probability that something will happen, good or bad. You could talk about the odds of winning the lottery, or the odds of an earthquake happening. But 'odds' are expressed differently from 'chance' and 'probability'. Odds are normally expressed like a ratio (eg 100:1), not a percentage as in your question.
A high probability, or a high chance, would mean that something is likely to happen. But 'high odds' means the opposite - that the chances against are high. The term 'odds' is predominantly used in gambling. High odds in gambling mean that the chances of winning are low, but in certain kinds of betting the payout would be higher as a result.
"Generally, the term high odds means that an outcome is less likely to happen. On the flip side, some players build their strategy on big prices, chasing better payouts." - Bookmakers
Although one might say that odds are "good" if they are favourable towards whatever it is you would wish to happen, don't confuse the word "great" with this. While "great" can mean good, in mathematics it means high. So, if someone said "the odds are great" that would idiomatically mean they were high, so the associated event is less likely to happen.
In your question you use percentages of chance, which, as I stated, are not the same. A 'high percentage chance' of something happening would mean that it is likely. You could still refer to the odds alongside the chance, but don't confuse the terminology between the two.