Extending Python list functionalities
You say you need the extra class, "due to how __sub__() was implemented"; because it returns a vanilla list, with a list comprehension. However, note:


If you replace e.g. 

return [elem - value for elem in self]


with:

return _BaseList(elem - value for elem in self)


__sub__ will return a _BaseList instead; and 
If you put those four methods in one class calling normalize would still work anyway, because you do convert to _BaseList after the subtraction.




In fact, three methods, because the __init__ is redundant - if all your subclass method does is call the superclass version, you can just let Python handle that for you.



The Zen of Python states that 


  Errors should never pass silently.


However, in both __truediv__ and __sub__, if value is not one of the three specified types (or it's a list of the wrong length), they quietly return None. Instead, you should raise TypeError if the user passes a value that can't be handled.



Speaking of specified types, don't write things like:

if type(value) in (int, float)


If you need to check types, use isinstance - this supports inheritance better:

if isinstance(value, (int, float)):


This is particularly important when you're using inheritance yourself - what happens if you try to subtract a _BaseList from another _BaseList? Python supplies abstract base classes that can help make this usage more generic.

Also note that there is another numeric type: complex - as Mathias Ettinger pointed out in the comments you can use Number when you want to cover all three cases.



There's a lot of duplication between the __sub__ and __truediv__ implementations; you could factor this out by extracting to a method that also takes the operator to apply, then use the operators defined in operator.



from collections.abc import Sequence
from operators import sub, trudiv


class Array(list):

    def normalize(self):
        min_ = min(self)  # calculate this once
        return (self - min_) / (max(self) - min_)

    def __sub__(self, other):
       return self._process(other, sub)

    def __truediv__(self, other):
       return self._process(other, truediv)

    def _process(self, other, op):
        if isinstance(other, Sequence):
            if len(other) == len(self):
                return Array(op(a, b) for a, b in zip(self, other))
            raise ValueError('cannot operate on a sequence of unequal length')
        return Array(op(a, other) for a in self)


In use:

&gt;&gt;&gt; a = Array((7, 8, 9))
&gt;&gt;&gt; a
[7, 8, 9]
&gt;&gt;&gt; a - 2
[5, 6, 7]
&gt;&gt;&gt; a - [1, 2, 3]
[6, 6, 6]
&gt;&gt;&gt; a.normalize()
[0.0, 0.5, 1.0]
&gt;&gt;&gt; a - 'abc'
Traceback (most recent call last):
  File "&lt;stdin&gt;", line 1, in &lt;module&gt;
  File "&lt;stdin&gt;", line 6, in __sub__
  File "&lt;stdin&gt;", line 12, in _process
  File "&lt;stdin&gt;", line 12, in &lt;genexpr&gt;
TypeError: unsupported operand type(s) for -: 'int' and 'str'
&gt;&gt;&gt; a - [1, 2, 3, 4]
Traceback (most recent call last):
  File "&lt;stdin&gt;", line 1, in &lt;module&gt;
  File "&lt;stdin&gt;", line 6, in __sub__
  File "&lt;stdin&gt;", line 13, in _process
ValueError: cannot operate on a sequence of unequal length


It might also be worth implementing __repr__, so you can tell more easily when you have a vanilla list and when you have an Array.