Probability of fluorescence: matching of binding energy and incoming radiation energy? Assume an X-ray diffractometer equipped with a copper anode X-ray tube. When a sample containing cobalt, iron, or manganese is irradiated by copper's K$\alpha_1$ radiation, sample fluorescence becomes significant.
I believe I read somewhere that when the incoming radiation's energy comes closer to the binding energy of the electrons, then the probability of fluorescence increases. Is this correct?
And also, can an inner-core electron's binding energy be approximated by the element's K$\alpha_1$ energy?
 A: I believe this relates to density of states and the shape of the bands.
When you try to excite an electron from one state to another, there needs to be an available state "upon arrival" - and the probability of the transition is therefore directly related to the density of states. If I'm not mistaken, this is the reason that the excitation is strongest when you hit the exact frequency of the gap.
As for your second question - the $K\alpha$ line is emitted when an electron drops from 2p to the 1s orbital. This is less than the binding energy of the electron, since the 2p state is still a bound state and therefore has a lot of associated binding energy.
A: 
[...]when the incoming radiation's energy comes closer to the binding
  energy of the electrons, then the probability of fluorescence
  increases. Is this correct?

When the incident energy is close to the binding energy there is a sharp increase in the absorption. See, for example, Figure 1-5 in the following document:
http://xdb.lbl.gov/Section1/Sec_1-6.pdf, especially the bottom panel that shows a nice sharp peak for Carbon around 300eV. Compare the above figure with the following table of electron binding energies: http://xdb.lbl.gov/Section1/Table_1-1a.htm.
  Because electrons must first be absorbed before fluorescence can occur, it is reasonable to say that the probability of fluorescence increases when the incident radiation is near the binding energy.

And also, can an inner-core electron's binding energy be approximated
  by the element's Kα1 energy?

Compare this table of $K\alpha_1$ energies: http://xdb.lbl.gov/Section1/Table_1-3.pdf, with the table of electron binding energies given above. In general you will find the X-ray Data Booklet (http://xdb.lbl.gov) very useful for this sort of work (you can even get a free hard copy). For example, this section (http://xdb.lbl.gov/Section1/Sec_1-2.html) explains emission lines. In the referenced section the symbols "$L_2$" and "$L_3$" mean the same thing as "$2p$" (respectively, $2p_{1/2}$ and $2p_{3/2}$, where the 1/2 and 3/2 refer to spin-orbit splitting), and the symbol "$K_1$" means the same thing as "1s". 
So, the short answer is: No, they are not the same, but are similar for light atoms. The $K\alpha_1$ energy is the energy difference between the $2p_{3/2}$ and $1s$ levels.
