There are 200 episodes in a season of Riddler Jeopardy!. The first episode of the season features three brand-new contestants. Each subsequent episode includes a returning champion (the winner of the previous episode) as well as two new challengers.
Throughout the season, it so happens that the returning champions are particularly strong, with each one winning five consecutive episodes before being dethroned on the sixth.
If you pick a contestant at random from the season, what is the probability that they are a Riddler Jeopardy! champion (meaning they won at least one episode)?
Each winner wins five consecutive episodes, so there are 40 winners. 39 of them will lose on their 6th appearance. The 40th winner wins the 200th. This leaves 361 one-time losing contestants.
Counting each contestant's appearance, the probability would be $\dfrac{239}{600}$. However, I think it is implied picked from a roster of all from the season, so I am going with
$$\dfrac{40}{401}$$