The dilemma is that the probability is based on the actual defect rate of the lot. Which you cannot know from sampling. The probabilities are based on what would happen if you sampled the same lot many, many times. It is accurate on average over the long run...it is not accurate for any individual lot. The best you can do is to share the OC curve of the sampling plan you use. That describes the range of probabilities associated with various actual defect rates...
Some people also forget that the AQL is the acceptable defect rate that will be accepted 95% of the time...they think it is the defect rate that will be rejected 95% of the time...
The worst part is that a non-homogenous distribution of defects in the lot cannot be overcome by random sampling. So non-homogeneity increases the actual probability of 'missing' a 'bad' lot.
The other factor is the measurement error which is also rarely accounted for. Every measurement system, including visual inspection, has measurement error. The OC curves 'assume' that no measurement error exists...
Simply put, sampling is imperfect. Improving the quality so that defects are very rare is the only reliable way of knowing if you have an acceptable lot or not...