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```from numbers import Real

class ProbDict(dict):
"""A dictionary serving as a probability measure."""

def __init__(self, items = None):
"""Create a dictionary from iters.

If items can't be fed to a dictionary, it will be interpreted as a
collection of keys, and each value will default to value 1/n. Otherwise,
the values are normalized to sum to one. Raises ValueError if
some values are not numbers or are negative.

Arguments:
- `items`: argument with which to make dictionary

"""
if items is not None: return dict.__init__(self)
try:
# can fail if items is not iterable or not full of size 2 items:
dict.__init__(self, items)
except TypeError:
try:
# Let's assume items is a finite iterable full of keys
vals = [1/len(items)] * len(items)
except TypeError:
# Apparently items has no length -- let's take it as the only
# key and put all the probability on it.
dict.__init__(self, (items, 1))
else:
# if items has a length, it can be iterated through with zip
dict.__init__(self, zip(items, vals))
else:
# we've successfully made dic from key, value pairs in items, now let's
# normalize the dictionary, and check the values
for v in self.values():
if not isinstance(v, Real):
raise TypeError("Values must be nonnegative real numbers so I " +
"can properly normalize them. " + str(v) + " is not.")
elif v < 0:
raise ValueError("Values must be nonnegative, unlike " + str(v))

tot = sum(self.values())
for k, v in self.items(): self[k] = v/tot

def __setitem__(self, key, value):
# Overridden to make sure dict is normalized.
if not isinstance(value, Real) or value < 0 or value > 1:
raise ValueError("Value must be a number between 0 and 1, unlike " +
str(i))
try:
r = (self[key] - value)/(1 - self[key])
# r is the fraction of the remaining probability mass that
# we're going to give up (take).
for k in filter(key.__ne__, self):
dict.__setitem__(self, k, self[k] * (1 + r))
value = value if len(self) != 1 else 1
if value:
dict.__setitem__(self, key, value)
else:
# This is the purging stage!
dict.__delitem__(self, key)
except ZeroDivisionError:
# self[key] = 1, so key has all the probability mass. We'll leave it
# as is, since there's no sensible way of reducing it.
pass

def __delitem__(self, key):
# Deleting frees up probability mass!
self[key] = 0
# Note that __setitem__ handles the deletion for us.

def __missing__(self, key):
# Accessing an inexistent key gives 0 rather than error, but
# does not create key, val pair (unlike defaultdict)
return 0
```