Being exposed once to a small amount of Asbestos is unlikely to harm you to the point of killing you.
But when working around Asbestos you need to wear a mask that has filters on it and wear gloves as well to prevent the Asbestos from getting into your lungs.
If you think you've been exposed to Asbestos it's best to see a doctor about it although in most cases it takes many, many years to feel the affects of the Asbestos exposure.
The people that do get Mesothelioma from Asbestos Exposure are usually the people that have worked for years in places such as shipyards or other places that had high levels of Asbestos years ago that they were exposed to.
Then years later they get diagnosed with the deadly disease Mesothelioma from the Asbestos.
If you have Asbestos in your home or workplace avoid touching or disturbing it and if possible get a professional to come in and remove the Asbestos.