what are the chances of catching a Sylesti?

It's kind of random. ^.^ There ARE rumors that if you lower a sylesti's health, it may give you a higher chance of catching them, though.

Sadly, there is never a guarantee of catching a sylesti unless you use a masterful snare trap but those require diamonds. There are things you can do to increase your chance of catching it but they can always run.
1) You can always try to lower the health but be very careful that you do not accidentally kill the sylesti. Use the block option if you are able so that your damage pets do not touch it. Note: the effect of this is fairly small.
2) Use a snare of a higher rarity than the pet you are trying to catch so using a standard snare for an uncommon pet or a strong snare for a rare sylesti. This is more effective than reducing health but it can fail same as any other snare.

Hope this helps and remember than it is always a matter of luck so you are not doing anything wrong.

Best of luck catching sylestis you want ^_^