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The documented behavior of io.BufferedReader.peek([n]) states:
peek([n])
Return 1 (or n if specified) bytes from a buffer without advancing the 
position.
Thereas the parameter n is the _max_ length of returned bytes.
Implementation is:
 def _peek_unlocked(self, n=0):
 want = min(n, self.buffer_size)
 have = len(self._read_buf) - self._read_pos
 if have < want:
 to_read = self.buffer_size - have
 current = self.raw.read(to_read)
 if current:
 self._read_buf = self._read_buf[self._read_pos:] + 
current
 self._read_pos = 0
 return self._read_buf[self._read_pos:]
Where you may see that the parameter n is the _min_ length
of returned bytes. So peek(1) will return _not_ just 1 Byte, but the
remaining bytes in the buffer.