Constant density on a finite interval

For X~Uniform(a,b), a<b, f(x)=1/(b-a) inside the interval and 0 outside. For a≤c<d≤b, P(c<X<d)=(d-c)/(b-a). All equal-length subintervals have equal probability, but an exact single point has probability zero. F(t)=0 below a, (t-a)/(b-a) between a and b, and 1 above b.