probability of drawing

[RJT]

I assume the following is invalid logic, because I have never heard/read it discussed. What is the flaw? Or is it logical, but impractical?

I will use a flush draw for an example. I also use % for brevity.

10 player table
Player 1 pocket is suited –say hearts.
Flop is heart- heart-club

Probability to draw a heart on turn: 9/47 =19.15%
No heart on turn, then probability to draw heart on river: 9/46=19.56%

But in reality, there are 18 cards already dealt(9 other players x 2). There almost certainly is at least one heart in the batch of 18 and more probably 4.5 hearts already dealt(18 divided by 4 suits).

Why don’t we calculate chance to draw heart on turn as either:
9-4.5/47=9.57% or 9-4.5/29=15.52% (29= 47-18)

Chance to draw heart on river as either:
9-4.5/46=9.78% or 9-4.5/28=16.07%