That looks like a healthy battery, cycle count is relatively low at 186, should be good to around 1,000, the Condition is Normal which it should be unless there is a problem, and a Capacity of 5903 mAh is not far below the as-built capacity of the battery. All batteries drop in capacity as they are used but yours is still good.
It is confusing why that battery should discharge so quickly with a minor load be placed on it. Try charging fully, and then just time the battery life one day so you have an accurate estimate of the charge life.
You can also reboot the Air before doing that to make sure there are no processes running in the background...sometimes things like web surfing and e-shopping end up starting things from the sites visited that run in the background and eat resources.
You can check that by going to Applications > Utilities > Activity Monitor and see what the load is on the CPU...just idling, not having started anything it should be was down in the single digits. If it shows a high CPU percentage, then you have something running in the background eating your power. If that is the case, you can look at the listing of Processes and see what is using the high CPU percentage, then ask about killing that process...be sure to ask first so you don't stop something you actually need to have running.
One last thought, have you by any chance installed anti-virus software of some sort? Those programs run and really, really eat resources.