He's not expecting it, and so the vision triggered by her question takes Obi-Wan completely by surprise. He's studied for countless hours with Master Yoda in order to keep his prescience at bay, but so much talk and thinking of the future has clearly weakened his mental barriers: he sees a young man and woman, celebrating, victorious. The woman has dark hair and an infectious smile; the man has light, sandy hair, so reminiscent of another, and is more solemn, even as he smiles happily as well. He glances back as the woman - his sister, Obi-Wan is sure - pulls him back to the celebration, and he's also sure that the man is looking directly at him.

It doesn't give him the answer to Padmé's question, but it certainly gives him hope.

"Your grandchildren will grow up in a Republic, not an Empire," he says with surety giving his words weight. "We will both do what we must to ensure that your children, and their children, know us."