The brain is constantly acquiring information and responding to it, as an intelligent information processor the brain is able to respond to changing conditions as the information is acquired. Adjusting to conditions milliseconds after they occur. Re, your example, the brain estimates probability based on past experience, how long a light stays green, travel speed, etc, which determines whether you must stop or there is sufficient time to cross before the light turns amber or red.
What happens on any occasion is determined by an interaction of multiple elements, speed, distance, light cycle times, urgency, mood, etc, which come together as an action performed: on this occasion you stop as the light turns amber.
Just to clarify, in the example the light was already red, so you slowed down, even though it actually did change to green at the last minute. Your determinist passenger asked "Why you slow down?" and you said that the light could have remained red, even though it did not remain red, but instead it change to green as you arrived. But the determinist argues that it was impossible for it to remain red, because it was destined to be green since the Big Bang. So he asks again, "Why did you slow down?"
If I'm reading your response correctly, you are pointing out that the brain is a complex organ that "is constantly acquiring information and responding to it, as an intelligent information processor".
And that, "the brain estimates probability based on past experience". So, you knew that the light could have remained red even though it actually did turn green just as you arrived at the traffic light. Despite the fact that it would not remain red, it still could have remained red.
Given that traffic lights are designed to cycle in order to allow traffic flow, the likely reason why it would stay red is a malfunction. Malfunctions not being common, not a daily or weekly or even monthly occurrence there is no reason to react as if is going to happen even though we know it can happen. A driver reacting as if the light is likely to, or going to stay red because sometimes lights malfunction is responding unreasonably: a brain glitch.
Given experience with the world, we understand the probability of things happening, car crashes, lighting strikes, power outages, a traffic light staying red and so on....