Mark has rightly pointed.
You may think like this, If there is high probability price would go up in future(in very short period), lets say 90% then investors would continue to buy until they no longer expect price to increase with such a high probability. Or until this strategy of buying shares with high probability of going up is not profitable(excess risk adjusted return).
Similarly, if there is very high probability that price will fall in future, then investors would continue to sell until they no longer expect price to fall beyond that level. Or until this strategy of selling shares with high probability of going down is not profitable(excess risk adjusted return).
So your question : is it realistic to assume that current price of stock takes into account probability of going up and down in the future? Answer is completely yes. After all price are not deterministic.
Lets come to your dilemma on pricing of option contract. Since derivatives derive their value from some underlying assets it is completely realistic to assume that current price of security is fair( only for actively traded) and hence does not require to take into account expected return on the underlying one.
I hope it would help you to understand.