Wrong, wrong, wrong! I don't know why you think a coin has "memory" and can adjust its own 'heads' probability as time goes on. No: if it is a fair coin, the probability that (before doing any tosses) your first 9 tosses will be all heads is (1/2)^9. However, if your first 9 tosses did happen to be all heads, that would not affect the probability of getting heads again; that probability remains 1/2. As LCKurtz has indicated, for a coin that you suspect might not be fair (so for which you do not actually *know* the head/tail probabilities), seeing 9 heads in a row may cause you to change your mind somewhat about P{head}. The coin itself is completely unaffected; what IS affected would be your "state of knowledge" about the coin.
If you just reach into your pocket and pull out a standard coin, its head/tail probabilities are going to be essentially 1/2. A "rigged" coin might have head/tail probabilities different from 1/2, but even then the probabilities would not be affected by the outcomes of some initial tosses. For example, even if I have a weighted coin with P{Head} = 0.6 and P{Tail} = 0.4, the probability of my first 9 tosses being all heads is (0.6)^9; the probability that the 10th toss is heads is still 0.6, no matter what happened in tosses 1--9.
So, given all this, why do we say that our state of knowledge could ever be toss-dependent? Well, if you are a 'Bayesian' (which I, personally, am...more-or-less), you would start by saying that the coin has some fixed, but unknown probability P{head} = p, and where p itself is subject to a probability distribution f(p) (such as uniformly distributed between 0 and 1). For a uniform prior, our a priori probability of heads on one toss is 1/2. However, after getting our first n tosses as all heads, out new expected probability of getting a 'head' is now 1/(n+1). So, I my first 9 tosses were all heads, my new head probability estimate would be 1/10.
I was somewhat reluctant to mention any of the Bayesian stuff because I am not convinced you fully grasp yet how probabilities actually work. I can only hope that I have not confused you.