How do you norm a histogram in python?

This is a follow-up question to this answer. I'm trying to plot normed histogram, but instead of getting 1 as maximum value on y axis, I'm getting different numbers.

For array k=[1,4,3,1]

 import numpy as np

 def plotGraph[]:
   
    import matplotlib.pyplot as plt
    
    k=[1,4,3,1]

    plt.hist[k, normed=1]

    from numpy import *
    plt.xticks[ arange[10] ] # 10 ticks on x axis

    plt.show[]  
    
plotGraph[]

I get this histogram, that doesn't look like normed.

For a different array k=[3,3,3,3]

 import numpy as np

 def plotGraph[]:
   
    import matplotlib.pyplot as plt
    
    k=[3,3,3,3]

    plt.hist[k, normed=1]

    from numpy import *
    plt.xticks[ arange[10] ] # 10 ticks on x axis

    plt.show[]  
    
plotGraph[]

I get this histogram with max y-value is 10.

For different k I get different max value of y even though normed=1 or normed=True.

Why the normalization [if it works] changes based on the data and how can I make maximum value of y equals to 1?

UPDATE:

I am trying to implement Carsten König answer from plotting histograms whose bar heights sum to 1 in matplotlib and getting very weird result:

import numpy as np

def plotGraph[]:

    import matplotlib.pyplot as plt

    k=[1,4,3,1]

    weights = np.ones_like[k]/len[k]
    plt.hist[k, weights=weights]

    from numpy import *
    plt.xticks[ arange[10] ] # 10 ticks on x axis

    plt.show[]  

plotGraph[]

Result:

What am I doing wrong?

We can normalize a histogram in Matplotlib using the density keyword argument and setting it to True. By normalizing a histogram, the sum of the bar area equals 1.

Consider the below histogram where we normalize the data:

nums1 = [1,1,2,3,3,3,3,3,4,5,6,6,6,7,8,8,9,10,12,12,12,12,14,18]

nums2= [10,12,13,13,14,14,15,15,15,16,17,18,20,22,23]

fig,ax = plt.subplots[] # Instantiate figure and axes object

ax.hist[nums1, label="nums1", histtype="step", density=True] # Plot histogram of nums1

ax.hist[nums2, label="nums2", histtype="step", density=True] # Plot histogram of nums2

plt.legend[]

plt.show[]

Normalized histogram:

matplotlib.pyplot.hist[x, bins=None, range=None, density=False, weights=None, cumulative=False, bottom=None, histtype='bar', align='mid', orientation='vertical', rwidth=None, log=False, color=None, label=None, stacked=False, *, data=None, **kwargs]

import matplotlib.pyplot as plt

x = [1, 9, 5, 7, 1, 1, 2, 4, 9, 9, 9, 3, 4, 5, 5, 5, 6, 5, 5, 7]
plt.hist[x, density = True, color = "green", label = "Numbers"]
plt.legend[]
plt.show[]

How do you create a normalized histogram?

How do I normalize a histogram in Matplotlib?

How do you fit a normal distribution to a histogram in Python?

How do you normalize data in Python?