The Milky Way is about 100,000 light years in diameter and about 1,000 light years thick. Its volume is therefore roughly 7.9 trillion cubic light years. (This assumes a cylindrical shape, and neglects the central bulge; see the note at the end of the paragraph.) A sphere with a radius of 1,000 light years has a volume of approximately 4.2 billion cubic light years. That's less than one tenth of one percent
of the overall volume of the galaxy. The actual figure is about .05 of one percent. (If the whole central bulge were counted, then that fraction would be even smaller.)
Of course, stars are not evenly distributed. By http://imagine.gsfc.nasa.gov/docs/as...s/980123d.html
, there are approximately 14,600 stars within 100 light years of Earth. If we assume that stars are distributed with the same density out to 1,000 light years, then, extrapolating outward, there are about 10^3 as many stars, or roughly 14,600,000 stars within 1,000 light years of Earth. (The sun is probably less than 100 light years from the galactic plane.) The presently accepted figure of the number of stars in the Milky Way galaxy is conservatively 100 billion. Therefore, within 1,000 light years of Earth are only about one percent of one percent
of all the stars in the galaxy.
However you slice it, it is highly premature to say that life is rare, just because there's no sign of it in our immediate stellar neighborhood.