I saw a TEDx talk the previous day about the LIGO experiment and in that video he said they are waiting for the day Jan 1st 2017 for the Ripple in Gravity caused by two black holes colliding each other to reach us. But how could they make such an estimation? How the scientist knew about some incident happened 1.3 billion years ago?
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Right so what you have misunderstood is that this was a statistical prediction about when the first detection might be made, based on assumptions about the number of possible sources in the universe and their distance from us.
It is mildly surprising that (advanced) LIGO found such a big signal so soon after it began operations.
Detecting a few more will start to tell us a lot about how many large black holes there are in the universe as a function of cosmic time. Because the signal strength scales as 1/distance and binary mass to the power of 5, whilst the number of massive stars scales as $M^{-2.3}$ I think one expects most detections to be from distant very massive objects if their density is uniform in time.
The latter can be inferred because the signal strength and frequency from binary mergers tells you how far away they are, and GWs travel at the speed of light.
ProfRob
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