<p>I wish to address the general question of fabricating unusual $\TeX$ symbols. $\newcommand{\ConditionallyIndependent}[3]{#1 \perp\kern-5pt \perp #2 \mid #3}$</p>

<h3>The workaround</h3>

<p>The lack of a $\TeX$ symbol for your preferred notation is a strong indication that your notation is not well known.  At a minimum, then, <strong>please define and explain your notation on or before its first use.</strong></p>

<p>Now, given that such a definition is necessary,  why not adopt a more convenient notation instead?  Thus, you might write</p>

<blockquote>
  <p>Let $X \perp Y \mid Z$ mean that $X$ and $Y$ are conditionally independent given $Z.$</p>
</blockquote>

<p>instead of </p>

<blockquote>
  <p>Let $\ConditionallyIndependent{X}{Y}{Z}$ mean that $X$ and $Y$ are conditionally independent given $Z.$</p>
</blockquote>

<p>The first uses the standard $\TeX$ symbol <code>\perp</code> while the second is more involved.  The rest of this answer describes the second solution.</p>

<h3>When you must</h3>

<p>The only situation where such a solution would not be acceptable would be where you must emulate some other document.  If that "document" is a question you are answering or commenting on, and you wish to use its notation, then likely the solution already appears in the question itself: imitate that.  Otherwise, then either (a) the notation in the question is a mere image or (b) you wish to use notation from some authority or reference material.  In these cases several good options have been offered in other replies in this thread.  The principal objection is that most of them are unreadable in their raw form, creating problems for alternative rendering mechanisms (such as screen readers).</p>

<p><strong>Might I suggest the use of macros to solve this problem?</strong>  As an example, in the first line of this post I defined the following macro using Glen_b's $\TeX$ solution:</p>

<blockquote>
  <p><code>\newcommand{\ConditionallyIndependent}[3]{#1 \perp\kern-5pt \perp #2 \mid #3}</code></p>
</blockquote>

<p>(The syntax is briefly but adequately documented at <a href="https://www.math.uh.edu/~torok/math_6298/latex/macros.html" rel="nofollow noreferrer">https://www.math.uh.edu/~torok/math_6298/latex/macros.html</a>, <em>inter alia</em>, which you may read for more information.)</p>

<p>This definition did not result in anything being rendered: it is invisible to the reader.  Now, although a screen reader might render it, its initial parts will make it apparent to the listener what is being done: "he's defining a $\TeX$ macro called <code>ConditionallyIndependent</code>; I probably don't need to know the details."</p>

<p>Then, whenever this symbol is needed, it will be rendered in <em>all</em> forms (raw or interpreted) in a meaningful way.  The screen reader, for instance, will display the following line</p>

<p>$$\ConditionallyIndependent{X}{Y}{Z}$$</p>

<p>in its raw form as <code>\ConditionallyIndependent{X}{Y}{Z}</code>.  Not a bad compromise.</p>
