Ignore the three answers telling you that you have nothing to worry about because you do.
Today's nanny state is operating in over-drive and does not like it when someone doesn't conform. Common sense and reason are about gone now, especially when it comes to the children. Most juvenile probation departments take smoking seriously. Many are testing for nicotine if you are under 18.
Two to five days from last cigarette on the simple stick urine test, 7 to 10 days if they use the GC/MS, and up to 90 days if they use a hair follicle test.
If you test positive it's a violation of probation. At the least they will make you go through indoctrination classes. Repeatedly fail and it could have you put in juvie detention.
I wish I had better news for you but those are the facts.
Update: I can only give you anecdotal evidence; my girlfriend's 16 year old got caught up with juvenile justice system, was drug tested while on probation, tested positive for nicotine, was forced to take smoking cessation classes, kept violating probation by continually failing for nicotine, threatened by judge with lock down over matter for not stopping his smoking habits.
Granted much depends on where you live; high crime area and they have more important things to worry about, but in suburbs juvenile justice has too much time on their hands. A simple minor in possession of alcohol, weed or cigarettes these days leads to aggressive juvenile justice involvement. (In the old days the police in my area would just make us dump out alcohol when caught at 15 and send us on our way; no charges, no telling parents, nothing. And almost all of us grew up to be successful, contributing members of society. (And cigarettes were legal for kids to smoke so no problem there.) But now a days, get caught with alcohol at 15 or God forbid, cigarettes, and they make a federal case out of it! You are now branded a defect and the government has to safe you from yourself by forcing you into indoctrination programs. And it seems what juvenile justice spews out likely does more damage to many teens. They brand you an alcoholic or drug addict and your life isn't your own till 18 (or longer in some cases), so you don't want to get caught up in that mess.
You say that you only got 3 months probation; that's pretty light. Either you just saw the initial intake officer and he put you on an unofficial probation (whereby your case won't go in front of a judge if you stay out of trouble or you got real lucky and have a lenient judge. Either way run as far away from juvenile justice as you can(I don't mean literally runaway but rather stay out of trouble so you get off probation quick). Its real easy to get sucked into their web, and that's a place you don't want to be.
3 months isn't that long; pass your drug tests, stay out of trouble, and you will have your life back; partying, smoking and hanging out with your friends. But fail those drug tests (even for nicotine in many jurisdictions) and probation and treatment gets extended. And trust me you don't want juvenile justice in your life till 18; you won't have a fun childhood.
Good Luck
Ah yeah continue to ignore John J.'s rather pithy but inaccurate (and likely fictional story of juveniles smoking in front of detention centers) post, for although he tries to make himself appear knowledgeable on this subject, he knows not what he is talking about. Below is just one site of many explaining how lots of states are requiring probation nicotine testing on juveniles.
http://www.ehow.com/info_8405489_kinds-tests-do-courts-give.html
http://www.erowid.org/chemicals/nicotine/nicotine_testing.shtml