(The following is not meant to be serious mathematics.)
In decimal there are $1000$ three place numbers. The probability that at the $N^{\rm th}$ decimal place of $\pi$ the last three figures enounce exactly the number $N$ therefore is ${1\over1000}$, and the probability that this does not happen is ${999\over1000}$. Assuming independence of the involved events, the probability of failure at all decimals up to the $700^{\rm th}$, say, therefore comes to about $$\left({999\over1000}\right)^{700}<{1\over2}\ .$$ This means that we can expect such an event to happen in the first $700$ decimal places of $\pi$ with a probability $>{1\over2}$.