There's a lot of factors:
1.) The ball has it's own mass, thus, in order to move it, you need a sufficient amount of force.
2.) The table is not frictionless, no matter how slight it is, there's still some resistance being offered.
3.) Look at the angle of the hit, it's too slight (if the 3 ball was hit first). You need a greater angle than that in order to move the 3 ball.
The call was too close, it could either be the 3 or the 9. But because the 9 ball moved first, it's the safer and more reasonable choice.