$3$-player card game probability question

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Three people, (call them $C$, $D$, and $E$), decide to play a card game for fun. They use an ordinary fair deck of $52$ cards, shuffled well immediately before each hand is drawn, and randomly draw cards from it one a time without replacement, all $3$ using (sharing) the same drawn cards to determine who wins. A win is defined as follows:

$C$ wins if he gets at least one of all $13$ ranks of the cards (regardless of suit as they can be mixed suit or even all the same suit) in a hand.

$D$ wins if he gets either $6$ reds or $5$ blacks in a row (consecutive) for a particular hand. Each new hand starts with $0$ in a row so there is no "carryover" from a previous hand.

$E$ wins if she gets either $3$ Aces or $4$ of any "picture" card ($J$,$Q$, or $K$).

It is possible for ties to occur but the rule is any ties are awarded as a win for $C$, even if $C$ was not even close to winning the hand.

So the question is who has the highest probability of winning?