Shouldn't the probability of sampling a point from a continuous distribution be 0?

Hey I was reading about Gaussian EM algorithm in which you first calculate the likelihood of data points being sampled from a Gaussian and then adjust your mean and variance to maximize it. To calculate the probability of a point being sampled from a distribution we do

$P({x}_{i}\mid \theta )=\frac{1}{\sqrt{2\pi {\sigma}^{2}}}\mathrm{exp}\left(\frac{-({x}_{i}-\mu {)}^{2}}{2{\sigma}^{2}}\right)$

But how can you sample a point from a continuous distribution? Shouldn't this be zero? Moreover I read many times about sampling a point/data from some continuous distribution but I can't understand how could you do that as for continuous random variable X the $P(X={x}_{1})=0$, so how could yo sample data point(s) from a continuous distribution?

Or does this sampling have some other meaning. I've seen many questions on this platform but I couldn't get my answer.

Hey I was reading about Gaussian EM algorithm in which you first calculate the likelihood of data points being sampled from a Gaussian and then adjust your mean and variance to maximize it. To calculate the probability of a point being sampled from a distribution we do

$P({x}_{i}\mid \theta )=\frac{1}{\sqrt{2\pi {\sigma}^{2}}}\mathrm{exp}\left(\frac{-({x}_{i}-\mu {)}^{2}}{2{\sigma}^{2}}\right)$

But how can you sample a point from a continuous distribution? Shouldn't this be zero? Moreover I read many times about sampling a point/data from some continuous distribution but I can't understand how could you do that as for continuous random variable X the $P(X={x}_{1})=0$, so how could yo sample data point(s) from a continuous distribution?

Or does this sampling have some other meaning. I've seen many questions on this platform but I couldn't get my answer.