In Math problems on lotteries, it is traditionally assumed that 

    (1)  the numbers on a ticket are different (no repeating),

and

    (2)  the order of numbers on a ticket does not matter to determine winning.


If follow to the tradition in this current problem, it should be stated in the 
problem, that 


    +---------------------------------------------------------------------+
    |   tree integer numbers from 1 to 64 on a ticket are different       |
    |   (no repeating) and the order of the three numbers on the ticket   | 
    |                    does not matter.                                 |
    +---------------------------------------------------------------------+


Below is my solution to the problem in this formulation.


There are   =  = 41664 different possible triples of numbers.


Combining it with the separate integer number from 1 to 27, we have, in all,

     41554*27 = 1121958  possible outcomes (or tickets).


Only one of these tickets wins. So, the probability of winning is

    P = 1/1,121,958 =  = 8.91299E-07.


It is a standard pattern of analysing/solving traditional Math problerms on lotteries.

As you see, the analysis and my answer are significantly different from that by @Theo.