Feller's book was published in 1968. Mandelbrot said of Feller's illustration of the random walk ,"The curve looked like a mountain's profile or cross section, and the points where it intersects the time axis reminded me of certain records I was then investigating relative to telephone errors. " So other people have found the book inspiring. It is one of the most enjoyable books I have read.
Incidentally Chebyshev's inequality is on page 233 of Volume I. I'm using this fact to illustrate that there is less analysis then algebra in this first volume. By contrast , Chebyshev's Theorem is proved in Shirayaev's book on page 47, ( Apostol's book Calculus Volume II has a chapter on probability , ( Chapter 14) Chebyshev's inequality is proved on page 563. And I think a book on real analysis , ( Folland for instance) has a proof too, page 185) . So , be prepared for hard analysis if you pick up a copy of Shiryaev's book. Others can perhaps come up with more suggestions.