There are many ways to do this, but the simplest and probably fastest is with Numpy, which you should get accustomed to using with image processing in Python:
from PIL import Image
import numpy as np
# Load image and ensure RGB, not palette image
im = Image.open('start.png').convert('RGB')
# Make into Numpy array
na = np.array(im)
# Make all pixels of "na" where the mean of the R,G,B channels is less than 50 into black (0)
na[np.mean(na, axis=-1)<50] = 0
# Convert back to PIL Image to save or display
result = Image.fromarray(na)
result.show()
That turns this:

Into this:

Another slightly different way would be to convert the image to a more conventional greyscale, rather than averaging for the luminosity:
# Load image and ensure RGB
im = Image.open('start.png').convert('RGB')
# Calculate greyscale version
grey = im.convert('L')
# Point process over pixels to make mask of darker ones
mask = grey.point(lambda p: 255 if p<50 else 0)
# Paste black (i.e. 0) into image where mask indicates it is dark
im.paste(0, mask=mask)

Notice that the blue channel is given considerably less significance in the ITU-R 601-2 luma transform that PIL uses (see the lower 114 weighting for Blue versus 299 for Red and 587 for Green) in the formula:
L = R * 299/1000 + G * 587/1000 + B * 114/1000
so the blue shades are considered darker and become black.
Another way would be to make a greyscale and a mask as above. but then choose the darker pixel at each location when comparing the original and the mask:
from PIL import Image, ImageChops
im = Image.open('start.png').convert('RGB')
grey = im.convert('L')
mask = grey.point(lambda p: 0 if p<50 else 255)
res = ImageChops.darker(im, mask.convert('RGB'))
That gives the same result as above.
Another way, pure PIL and probably closest to what you actually asked, would be to derive a luminosity value by averaging the channels:
# Load image and ensure RGB
im = Image.open('start.png').convert('RGB')
# Calculate greyscale version by averaging R,G and B
grey = im.convert('L', matrix=(0.333, 0.333, 0.333, 0))
# Point process over pixels to make mask of darker ones
mask = grey.point(lambda p: 255 if p<50 else 0)
# Paste black (i.e. 0) into image where mask indicates it is dark
im.paste(0, mask=mask)

Another approach could be to split the image into its constituent RGB channels, evaluate a mathematical function over the channels and mask with the result:
from PIL import Image, ImageMath
# Load image and ensure RGB
im = Image.open('start.png').convert('RGB')
# Split into RGB channels
(R, G, B) = im.split()
# Evaluate mathematical function over channels
dark = ImageMath.eval('(((R+G+B)/3) <= 50) * 255', R=R, G=G, B=B)
# Paste black (i.e. 0) into image where mask indicates it is dark
im.paste(0, mask=dark)