Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n;:;C[0,t]{ ightarrow}mathbb{R}^{n+1}$ and $X_{n+1};:;C[0,t]{ ightarrow}mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 < t_1 < {ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{leq}p{leq}{infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{ldots},(v_r,x)){int}_{L_2}_{[0,t]}exp{i(v,x)}d{sigma}(v)$ for $x{in}C[0,t]$, where ${v_1,{ldots},v_r}$ is an orthonormal subset of $L_2[0,t]$, $f_r{in}L_p(mathbb{R}^r)$, and ${sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.