The experimental probability is calculated by taking the number of favorable outcomes (in this case, the number of chocolate cake samples) and dividing it by the total number of trials (the total number of cake samples).
Here, the number of chocolate cake samples is 3, and the total number of samples is 9.
\[ P(\text{chocolate}) = \frac{\text{Number of chocolate samples}}{\text{Total number of samples}} = \frac{3}{9} \]
Now, we can simplify the fraction:
\[ P(\text{chocolate}) = \frac{3 \div 3}{9 \div 3} = \frac{1}{3} \]
Therefore, the experimental probability that the next piece of cake taken will be chocolate is:
\[ P(\text{chocolate}) = \frac{1}{3} \]