The chance of it appearing is very high. Generally, it's the first thing to appear after Luca.

Entering and exiting the BB menu can change the prizes for a Tournament. You'll get a new Tournament every 8-9 times. If you want, you can save just before one is due to appear and soft-reset to change the prizes.

If you want to change the League prizes, you can either Reset Data (but then you lose your team, levels and techs), or choose 'Back' at the end of the 10th match without viewing the prizes, save, then check the prizes. Soft-reset to change them.