Hey Hey

Unfortunately, we don't know the exact drop rates.  

The way the campaign champions drop is that there's a first roll where it selects a category of rewards, once selected, in this case, champion rewards, it then proceeds to do a second roll for which champ you will receive, so in all your every time you have received a champ you have just lucked out, unfortunately, bear in mind the harder the campaign difficulty you do the higher the chance that the rare champs will drop(once the loot category is selected).

many thanks and good luck.