Based on prior knowledge, the feature "K_SH_POST" represents whether the patient experienced cardiogenic shock at the time of admission to the intensive care unit. To analyze its relationship with the presence of chronic heart failure, we need to assess how the values of this feature correspond to the cases of yes and no for chronic heart failure.

Without further information, it is difficult to predict specific values of feature "K_SH_POST" that are associated with chronic heart failure. However, we can still analyze the possible values of "K_SH_POST" for each target class.

Here is the dictionary representing the analysis of the relationship between the feature "K_SH_POST" and the presence of chronic heart failure:

```json
{
  "no": ["no"],
  "yes": ["yes"]
}
```

Note that since the feature is categorical, it is not necessary to specify all possible values of "K_SH_POST" in the dictionary. As long as we include at least one value in each list for the target classes, the dictionary is valid.

Thus, based on the available information, we can conclude that if the myocardial infarction complications data of the patient shows chronic heart failure, the value of feature "K_SH_POST" will be either "no" or "yes".