BUG: Incorrect levels of MultiIndex when creating a new DataFrame by dropping a row
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

<img width="1143" alt="image" src="https://user-images.githubusercontent.com/33289453/81488715-0c2db980-929f-11ea-9960-61d24d1ab44f.png">

```python

#%%
import pandas as pd
import numpy as np

#%%
df = pd.DataFrame(np.arange(16).reshape(4,4), index=pd.MultiIndex.from_arrays([list("AABB"), list("XYXY")]), columns=list("abcd"))
df

#%%
df.index, df.index.levels

#%%
df_new = df.drop(index="A")
df_new

#%%
df_new.index, df_new.index.levels

```

#### Problem description

[this should explain **why** the current behaviour is a problem and why the expected output is a better solution]
The levels of MultiIndex of DataFrame never change when creating a new DataFrame by dropping a row. When creating a new DataFrame, the levels should match the new MultiIndex.

#### Expected Output
df_new.index.levels 
    should be 
FrozenList([['B'], ['X', 'Y']]))

#### Output of ``pd.show_versions()``

<details>

[paste the output of ``pd.show_versions()`` here leaving a blank line after the details tag]

INSTALLED VERSIONS
------------------
commit           : None
python           : 3.7.7.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 19.4.0
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : None.UTF-8

pandas           : 1.0.3
numpy            : 1.18.1
pytz             : 2019.3
dateutil         : 2.8.1
pip              : 20.0.2
setuptools       : 46.1.3.post20200330
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : 2.4.4
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.1
IPython          : 7.13.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fastparquet      : None
gcsfs            : None
lxml.etree       : None
matplotlib       : 3.1.3
numexpr          : None
odfpy            : None
openpyxl         : 3.0.3
pandas_gbq       : None
pyarrow          : None
pytables         : None
pytest           : None
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : 1.2.0
xlwt             : 1.3.0
xlsxwriter       : None
numba            : None

</details>
