The probability any sequence of length d is found in N digits of pi is 1 - 1/exp(N*0.1^d) (Poisson distribution for approximating the binomial). Then the limit as N approaches infinity is 1 for any finite d.
A simple example: 2 binary digits in binary sequences of length 3. There are eight binary sequences of length 3:
000
001
010
011
100
101
110
111
Of course, none of this matters, especially not when d << N, which it will be if N goes to infinity.
Also, the mathematical term is 'normal number' (http://mathworld.wolfram.com/NormalNumber.html), and we do not know whether pi is normal.
One way to see it is this: The probability of picking any particular point in the interval is 0. But that doesn't mean that picking that point is impossible. _Some_ point has to show up when you pick one at random.