Sure, here's a Python test case generator for the given problem statement "The Castle":

```python
import random

def tcgen():
    # Generate m and n
    m = random.randint(1, 16)
    n = random.randint(1, 16)
    
    # Generate the probabilities
    probabilities = [[round(random.uniform(0, 1), 3) for _ in range(n)] for _ in range(m)]
    
    return m, n, probabilities

# Function to print the generated test case in the appropriate format
def print_test_case(m, n, probabilities):
    print(m, n)
    for row in probabilities:
        print(" ".join(f"{p:.3f}" for p in row))

# Generate a test case
m, n, probabilities = tcgen()
print_test_case(m, n, probabilities)
```

This script generates random test cases for the problem "The Castle". Here's a breakdown of what it does:

1. It first generates random values for `m` and `n` within the given constraints (1 ≤ m, n ≤ 16).
2. It then creates a list of lists to store the probabilities that each cat (up to `m` cats) has of defeating each enemy in the rooms (up to `n` rooms). Probabilities are randomly chosen real numbers between 0 and 1, rounded to 3 decimal places.
3. The `print_test_case` function formats the generated test case appropriately for input to the problem.

To use this test case generator, you can simply call the `tcgen` function, and it will return `m`, `n`, and the `probabilities` list. You can then use the `print_test_case` function to print these values in the desired format.