# Instruction
You will be presented with a Python coding question along with a potential solution. Your task is to deconstruct the given solution into smaller, manageable modules. Each module should be clearly defined with specific function names, detailed input/output specifications, and concise function descriptions. Do NOT repeat the functions in the One-Shot Example.

## One-Shot Example
### Python Question:
Explore the frequency of lowercase alphabetical characters within the provided string using various analytical approaches to address complex and nuanced scenarios.

### Potential Solution:
```python
# Sample string
input_string = "This is a sample string with various lowercase characters such as a, b, c, etc."

# Using a dictionary to store character frequencies
def count_characters_dict(input_string):
    char_freq = {}
    for char in input_string:
        if char.islower():
            if char in char_freq:
                char_freq[char] += 1
            else:
                char_freq[char] = 1
    return char_freq
```

### RESPONSE:
1. Function to Normalize Input String
```python
def normalize_string(input_string: str) -> str:
    """
    Description:
        Normalizes the input string by removing non-alphabetical characters
        and converting all characters to lowercase.
    Parameters:
        - input_string (str): The string to be normalized.
    Returns:
        - str: A lowercase string with only alphabetical characters.
    """
```

2. Function to Count Character Frequencies
```python
def count_character_frequencies(normalized_string: str) -> dict:
    """
    Description:
        Counts the frequency of each lowercase alphabetical character
        in the normalized string.
    Parameters:
        - normalized_string (str): The string with lowercase alphabetical characters.
    Returns:
        - dict: A dictionary with lowercase characters as keys and their frequencies as values.
    """
```