You may think, you should buy a probe to calibrate your display. There are several products to buy around 100$ -1000$ with some software included. But what you get, is not only a fake, you may get worse results then it defaulted from the factory, especially when the monitor is more professional it is high risk to change from reference quality to class 3 or worse.
Most cheap probes are colorimeters. Those are very similar to camera sensors based on RGB color filters. You may have recognized, that camera sensors often see colors from different monitors different even if they look identical to you. The reason is: different monitors have different spectral properties. To describe it simply: you are measuring wrong values. Additional to that, cheap probes are not temperature stable. If you try to measure several thousands of colors, the probes will warm up by the display's energy. So if you measure the same color after e.g. 30 or 120 min again, you will measure different values.
Another big fake is, that most simple calibration software does not give you the ability to set up the target gamut. So you do not realize, that you measure a P3 gamut but you may want to work with REC709. After the "calibration" you are still in the gamut of the display/or used display preset e.g. laptop displays from apple are not sRGB/REC709, but your target audience is YouTube then you need REC709 and not P3.
In most cases not. Many displays meet the limits of the colorspace gamut like REC709, which means, they hit 100% of the gamut. But that does not mean, all colors inside of the gamut are located at the right position. Your cheap calibration software mostly only calibrates 2 dimensional and only the white point. But this most of the time does not correct many other wrong color locations. And if only the white point will be corrected, then the limits of the colorspace may still be wrong, like described with the laptop displays.
I can tell you this story because I myself bought all cheap probes and many new generations of them until I realized what is not working with them and why it does not work out. It took years of research and learning curve and many thousands of bugs to get here. Professional calibration stuff will cost around 25.000$ to deliver reliable results. I have many customers, who have bought something from Xrite or Data Color and realized that they could not match different monitors like there iMac Display to the Video Monitor. Try it yourself, but you will waste your money.
Only high-end Spectroradiometers with good spectral resolutions are able to correct the colorimeters bad color recognition of different spectral properties from different display technologies (like OLED, PLASMA, LCD, etc.), but you need to do this every time for every display... If you buy cheap probes with better software and calibration presets for different display types, you will still fail if you want to achieve reference quality or if you want to match different displays (like reference vs client monitors).