See, and that's where I think you're wrong. The chance an object is going to hit a target isn't determined by its acceleration like you describe it is. You could say that its trajectory will be more affected by Jupiter than by Earth, which will mean that it'll probably pass by Jupiter closer (only a little, mind you) than by Earth, and will move away from Jupiter at a greater angle with the original trajectory than from Earth, all other circumstances being equal. But an object would have to be moving very slowly, or have a trajectory *very* close to it for the gravitational force to actually make it collide with the planet at all.
Again, without doing the calculations (which I'd be hard-pressd to do correctly, by the way, although I do have a BSc in physics) I'd say the cross section is the major factor here, which would make an impact on Earth much more likely than the 1:300,000 you project.