Probability and Odds are two different things.

Probability is defined as:

P(Event) = Chances For Event Happening / Total Chances

Odds are defined as:

Odds(Event) = Chances For Event Happening : Chances Against Event Happening


So P(E) = 1 / 1000 for the first drawing; P(E) = 1 / 999 for the second drawing ...

Odds(E) = (1/999) * (1/998) * (1/997) * (1/996) * (1/995) = 5/985 or 1:197


In a nutshell odds are showing you a ratio of chances to win TO chances to loose. Probability is showing you chances to win TO total possible outcomes.