Assuming Illinois is tied with Minnesota and Wisconsin all with a 6-3 record at the end of the regular season, that would mean the following:
- Illinois beats Iowa and Northwestern
- Minnesota loses to Iowa, Northwestern, and Wisconsin
- Wisconsin beats Iowa, and loses to either Nebraska or Purdue and beats the other
According to the Big Ten Conference website, here are the procedures for determining tie breakers:
The following procedure will determine the representative from each division in the event of a three team tie:
If three teams are tied, steps 1 through 8 will be followed until a determination is made. If only two teams remain tied after any step (or sub-step), the winner of the game between the two tied teams shall be the representative. If three teams remain tied after any step, move to next step in tiebreaker with remaining tied teams.
1. The records of the three tied teams will be compared based on winning percentage in games between the tied teams.
Since all three of the teams would have a 1-1 record against each other, we can't determine anything based off of this step, so we move to the next one.
2. The records of the three tied teams will be compared based on winning percentage within their division.
Illinois would be 4-2 against B1G West opponents.
Wisconsin would be 4-2 against B1G West opponents.
Minnesota would be 3-3 against B1G West opponents.
Since Minnesota would be removed from the equation after having a worse record than both Illinois and Wisconsin, it comes down to head-to-head between Illinois and Wisconsin. Thus, Illinois would be the B1G West champion due to their win against Wisconsin.
There are 6 more steps, but they wouldn't need to be followed.
To reiterate,
the only way Illinois can win the B1G West is if the following things happen:
- Illinois has to win outright,
- Minnesota has to lose outright, and
- Wisconsin has to beat Minnesota and split between Nebraska and Purdue.
You can make up your own mind on the likelihood of any or all of those things happening.