def get_P_X_past_cond_X(past_symbol_counts, number_of_symbols):
    """
    Compute P(X_past | X), the probability of the past activity conditioned
    on the response X using the plug-in estimator.
    """
    
    P_X_past_cond_X = [{}, {}]
    for response in [0, 1]:
        for symbol in past_symbol_counts[response]:
            P_X_past_cond_X[response][symbol] \
                = past_symbol_counts[response][symbol] / number_of_symbols[response]
    return P_X_past_cond_X