"Little", but not "zero."
Fr. R. Barron goes through the exercise, and concludes that this ....whatever it is.....doesn't meet the criteria. Although the first four criteria are (arguably) satisfied,....
...The Catholic just war tradition teaches that a war can be legitimately waged if and only if there is a reasonable hope of success on the part of the government that authorizes the fighting. For example, a war fought against an overwhelmingly more powerful opponent might be noble and brave, but it wouldn’t be just. But another reason for questioning the reasonable hope of success is the absence of a clearly defined mission and purpose. As I stated above, if we don’t know precisely what it is that we’re fighting for, we cannot, even in principle, determine when and whether we’ve won. A poorly-defined war is one that enjoys no reasonable hope of success. I believe that the strict application of this final criterion would render our action in Libya unjust.
And he then cites Gen. Colin Powell as part of his argument.