Thanks for commenting.
The sun player only has to match the SUIT of the ally's card to recruit them as a companion, not the value.
The chance to for all 3 of the sun player's cards to not match the ally's suit is (3/4)*(3/4)*(3/4) = 27/64 = 0.422 = 42.2%
Therefore, the chance for one of the sun player's cards to match the suit is 1-0.422 = 0.578 = 57.8%
The chance is even higher if you have companion cards to sacrifice.
Let's assume the players have played through 8 rounds, and recruited 4 companions with slightly less than average luck. Also assume that they have fulfilled 3 out of 4 of the conditions, meaning that 1+3 = 4 cards are dealt out. The lowest of those card is the gloom value.
The chance for all 4 cards to be higher than 4 is (9/13)^4 = 23.0%
Therefore, the chance for the group to get either the "okay" or "good" ending is 77.0% in a typical game with 4 companions. With some luck and companion cards to sacrifice and/or achieving all 4 conditions, the percentage is even higher.