On one day,billions of people sees lights from real nuclear explosion, but they don't escape and even have no fear for that, just continue their life as usual, why?
The sun is a constant nuclear reaction
I don't know whether it qualifies as an explosion, per se.
Maybe you could be thinking of a solar flare?
Or perhaps (similar to the answer @boboquack gave):
They are looking at the light from a supernova?
I don't know that a billion people would be looking at it - nominally they could, since it'd likely look like a star in the sky, but how many people can/do look at stars...?
They would not be scared:
Because the supernova itself happened a long time ago - the light took until now to reach Earth, but the event itself is long past.
Of course, there are a bunch of other explanations:
Because they didn't notice that the supernova was different from any other star... because they knew the supernova was far, far away from Earth... etc.
Well, perhaps they
are watching recorded videos of the atomic bombs dropped on Hiroshima and Nagasaki of Aug.6th / 8th 1945...in their television sets :-)