Newcommand with single and double argument (probability function)

Question

I want to define a new command such that when a first and only argument is given it does one thing and when a second argument is given it expands the first argument. The idea is to replicate the probability function. One argument is for probability distribution and two arguments are for conditional probability distribution. I really don't know how to do it.
The (completed) following code
documentclass{article}
usepackage[utf8]{inputenc}
usepackage{amssymb}

newcommand{PP}[2]{???}

begin{document}

$PP{X}$

$PP{X}{Y}$

end{document}

should print

mathbb{P}{left({X}right)}
mathbb{P}{left({X}middle|{Y}right)}

I wouldn't like to have an optional argument because it would affect the order and readability of the code. I mean, I prefer PP{X}{Y} over PP[Y][X].
Could you please help me?
Thanks

egreg · Accepted Answer

You can do better, with a much easier user syntax.
documentclass{article}
usepackage{amsmath,amssymb}
usepackage{xparse}

ExplSyntaxOn

NewDocumentCommand{PP}{ s O{} >{SplitArgument{1}{|}}m }
 {
  mathbb{P}
  IfBooleanTF{#1}
   { PPauto #3 }
   { PPfixed {#2} #3 }
 }

NewDocumentCommand{PPauto}{mm}
 {
  left(
  IfNoValueTF{#2} { #1 } { #1 ;middle|; #2 }
  right)
 }

NewDocumentCommand{PPfixed}{mmm}
 {
  mathopen{#1(}
  IfNoValueTF{#3} { #2 } { #2 mathrel{#1|} #3 }
  mathclose{#1)}
 }

ExplSyntaxOff

begin{document}

[
PP{X} quad PP[big]{X} quad PP*{frac{X}{2}}
]
[
PP{X|Y} quad PP[big]{X | Y} quad PP*{frac{X}{2} | Y}
]

end{document}

The command PP has an optional argument for the size (never rely on left and right alone) or a * variant for the automatic sizing (use it only if really necessary).
The mandatory argument is split at |, if present. So the input code is much easier to read. Spaces around | are irrelevant.

Steven B. Segletes · Answer

I propose a syntax that uses a single argument only.  EDITED to include Mico's spacing suggestion.
documentclass{article}
usepackage{listofitems,amssymb}
newcommandPP[1]{%
  readlistarglist{#1}
  ifnum1=arglistlenrelax
    mathbb{P}{left(#1right)}
  else
    mathbb{P}{left(arglist[1];middle|;arglist[2]right)}
  fi
}
begin{document}
$PP{X}$

$PP{X,Y}$
end{document}

user108724 · Answer

Inspired of Werner's Answer and similar to Segletes's answer above:
documentclass{article}
usepackage{amssymb}
newcommand{pp}[1]{ppaux#1relax}
defppaux#1#2relax{%
  ifnumpdfstrcmp{#2}{}=0
      mathbb{P}{left(#1right)}
  else
    mathbb{P}{left(#1 ;middle|; #2right)}
  fi
}

begin{document}

$pp{X}$

$pp{XY}$

$pp{{XY}}$

end{document}

Newcommand with single and double argument (probability function)

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