At E3 2006 – six months after the Xbox 360 launched – Sony announced that the PlayStation 3 would cost $499 (20GB) and $599 (60GB). According to former Chief Xbox Officer Robbie Bach, this is when they knew they had a chance.
In an interview with IGN, Bach said they weren’t surprised by Sony’s decision to launch the PS3 in 2006, but when the price was announced, he was shocked:

The single moment when I knew we had real upside was when they announced the pricing at E3. I mean that was a total shock. We knew their product – their bill of materials – was too expensive but we thought they?d suck it up.

After talking about how they weren’t allowed in to see the presentation live, and had to watch it on a poor quality feed, Bach explained their reaction to the pricing announcement:
[…] Kaz said the price and the room we were in went silent. And I said, ‘Did he really say what I think he said"’ And so we started contacting people who were in the room to get confirmation that the price was actually the price he’d actually said. And when we confirmed that I said… ‘Oh, this could be really fun.’

Asked if he thought they won in that moment, Bach replied, “No… When you have 20% market share and they have 60, you never think you’ve won. That’s the kiss of death. But I did say, ‘Okay, we got a real chance, there’s real upside here, if we push hard we can reall...