It depends on the reason for the denial.

If it was denied for lack of supporting documentation, then a new application for a new purpose at a new consulate would probably have minimal issues from the previous denial.

If it was denied for misrepresentation or fraud (this is more common than one might think even if it may be unintentional - for example people often mention hotel references on their planned itineraries without actually making the bookings - the consulates DO check these references about 10% of the time), then there are more significant issues to be addressed.

In the case you reference, my experience leads me to believe that the following documentation should suffice :

a) an invitation from the trade show
b) a specific itinerary (does not have to be ticketed, only reserved) showing a return date from Italy (even if it involves a side trip to other Schengen countries)
c) sufficient funds to sustain the traveler/s in Europe (for Italy these are statutorily set amounts - see below for the details)
d) a permanent job in the home country (appropriate documentation from employer required) or in case of student the relevant enrolment documentation

A covering letter explaining the circumstances of the trip in bullet point format will also be very useful to the visa officer considering the application. If you are able to provide the above documents, you should have little problem establishing bonafides, even with the usually anal-retentive Italian consular officers.

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Statutory availability of funds required to be demonstrated to acquire a Schengen visa from Italian consular posts.

Single travelers

EUR 269.60 for upto 5 days
EUR 44.93/day for 5-10 days
EUR 51.64 + EUR 36.67/day for 11-20 days
EUR 206.58 + EUR 27.89/day for 21-89 days

Groups of travelers (per person)

EUR 212.81 for upto 5 days
EUR 26.33 for 5-10 days
EUR 25.82 + EUR 22.21/day for 11-20 days
EUR 118.79 + EUR 17.04/day for 21-89 days